{"id":468090,"date":"2026-02-11T13:25:17","date_gmt":"2026-02-11T13:25:17","guid":{"rendered":"https:\/\/www.newsbeep.com\/ca\/468090\/"},"modified":"2026-02-11T13:25:17","modified_gmt":"2026-02-11T13:25:17","slug":"heralded-high-dimensional-photon-photon-quantum-gate","status":"publish","type":"post","link":"https:\/\/www.newsbeep.com\/ca\/468090\/","title":{"rendered":"Heralded high-dimensional photon\u2013photon quantum gate"},"content":{"rendered":"<p class=\"c-article-references__text\" id=\"ref-CR1\">Vertesi, T., Pironio, S. &amp; Brunner, N. Closing the detection loophole in Bell experiments using qudits. Phys. Rev. Lett. 104, 060401 (2010).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.104.060401\" data-track-item_id=\"10.1103\/PhysRevLett.104.060401\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.104.060401\" aria-label=\"Article reference 1\" data-doi=\"10.1103\/PhysRevLett.104.060401\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2010PhRvL.104f0401V\" aria-label=\"ADS reference 1\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 1\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Closing%20the%20detection%20loophole%20in%20Bell%20experiments%20using%20qudits&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.104.060401&amp;volume=104&amp;publication_year=2010&amp;author=Vertesi%2CT&amp;author=Pironio%2CS&amp;author=Brunner%2CN\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR2\">Dada, A. C., Leach, J., Buller, G. S., Padgett, M. J. &amp; Andersson, E. Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities. Nat. Phys. 7, 677\u2013680 (2011).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nphys1996\" data-track-item_id=\"10.1038\/nphys1996\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnphys1996\" aria-label=\"Article reference 2\" data-doi=\"10.1038\/nphys1996\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 2\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Experimental%20high-dimensional%20two-photon%20entanglement%20and%20violations%20of%20generalized%20Bell%20inequalities&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fnphys1996&amp;volume=7&amp;pages=677-680&amp;publication_year=2011&amp;author=Dada%2CAC&amp;author=Leach%2CJ&amp;author=Buller%2CGS&amp;author=Padgett%2CMJ&amp;author=Andersson%2CE\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR3\">Malik, M., Erhard, M., Huber, M., Krenn, M., Fickler, R. &amp; Zeilinger, A. Multi-photon entanglement in high dimensions. Nat. Photon. 10, 248\u2013252 (2016).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nphoton.2016.12\" data-track-item_id=\"10.1038\/nphoton.2016.12\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnphoton.2016.12\" aria-label=\"Article reference 3\" data-doi=\"10.1038\/nphoton.2016.12\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2016NaPho..10..248M\" aria-label=\"ADS reference 3\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 3\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Multi-photon%20entanglement%20in%20high%20dimensions&amp;journal=Nat.%20Photon.&amp;doi=10.1038%2Fnphoton.2016.12&amp;volume=10&amp;pages=248-252&amp;publication_year=2016&amp;author=Malik%2CM&amp;author=Erhard%2CM&amp;author=Huber%2CM&amp;author=Krenn%2CM&amp;author=Fickler%2CR&amp;author=Zeilinger%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR4\">Martin, A. et al. Quantifying photonic high-dimensional entanglement. Phys. Rev. Lett. 118, 110501 (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.118.110501\" data-track-item_id=\"10.1103\/PhysRevLett.118.110501\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.118.110501\" aria-label=\"Article reference 4\" data-doi=\"10.1103\/PhysRevLett.118.110501\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2017PhRvL.118k0501M\" aria-label=\"ADS reference 4\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 4\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantifying%20photonic%20high-dimensional%20entanglement&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.118.110501&amp;volume=118&amp;publication_year=2017&amp;author=Martin%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR5\">Erhard, M., Malik, M., Krenn, M. &amp; Zeilinger, A. Experimental Greenberger-Horne-Zeilinger entanglement beyond qubits. Nat. Photon. 12, 759\u2013764 (2018).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41566-018-0257-6\" data-track-item_id=\"10.1038\/s41566-018-0257-6\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41566-018-0257-6\" aria-label=\"Article reference 5\" data-doi=\"10.1038\/s41566-018-0257-6\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2018NaPho..12..759E\" aria-label=\"ADS reference 5\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 5\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Experimental%20Greenberger-Horne-Zeilinger%20entanglement%20beyond%20qubits&amp;journal=Nat.%20Photon.&amp;doi=10.1038%2Fs41566-018-0257-6&amp;volume=12&amp;pages=759-764&amp;publication_year=2018&amp;author=Erhard%2CM&amp;author=Malik%2CM&amp;author=Krenn%2CM&amp;author=Zeilinger%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR6\">Erhard, M., Krenn, M. &amp; Zeilinger, A. Advances in high-dimensional quantum entanglement. Nat. Rev. Phys. 2, 365\u2013381 (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s42254-020-0193-5\" data-track-item_id=\"10.1038\/s42254-020-0193-5\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs42254-020-0193-5\" aria-label=\"Article reference 6\" data-doi=\"10.1038\/s42254-020-0193-5\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 6\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Advances%20in%20high-dimensional%20quantum%20entanglement&amp;journal=Nat.%20Rev.%20Phys.&amp;doi=10.1038%2Fs42254-020-0193-5&amp;volume=2&amp;pages=365-381&amp;publication_year=2020&amp;author=Erhard%2CM&amp;author=Krenn%2CM&amp;author=Zeilinger%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR7\">Designolle, S. et al. Genuine high-dimensional quantum steering. Phys. Rev. Lett. 126, 200404 (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.126.200404\" data-track-item_id=\"10.1103\/PhysRevLett.126.200404\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.126.200404\" aria-label=\"Article reference 7\" data-doi=\"10.1103\/PhysRevLett.126.200404\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2021PhRvL.126t0404D\" aria-label=\"ADS reference 7\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=4265518\" aria-label=\"MathSciNet reference 7\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 7\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Genuine%20high-dimensional%20quantum%20steering&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.126.200404&amp;volume=126&amp;publication_year=2021&amp;author=Designolle%2CS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR8\">Hiekkam\u00e4ki, M. &amp; Fickler, R. High-dimensional two-photon interference effects in spatial modes. Phys. Rev. Lett. 126, 123601 (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.126.123601\" data-track-item_id=\"10.1103\/PhysRevLett.126.123601\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.126.123601\" aria-label=\"Article reference 8\" data-doi=\"10.1103\/PhysRevLett.126.123601\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2021PhRvL.126l3601H\" aria-label=\"ADS reference 8\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 8\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=High-dimensional%20two-photon%20interference%20effects%20in%20spatial%20modes&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.126.123601&amp;volume=126&amp;publication_year=2021&amp;author=Hiekkam%C3%A4ki%2CM&amp;author=Fickler%2CR\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR9\">Chi, Y. et al. A programmable qudit-based quantum processor. Nat. Commun. 13, 1166 (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41467-022-28767-x\" data-track-item_id=\"10.1038\/s41467-022-28767-x\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41467-022-28767-x\" aria-label=\"Article reference 9\" data-doi=\"10.1038\/s41467-022-28767-x\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2022NatCo..13.1166C\" aria-label=\"ADS reference 9\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 9\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=A%20programmable%20qudit-based%20quantum%20processor&amp;journal=Nat.%20Commun.&amp;doi=10.1038%2Fs41467-022-28767-x&amp;volume=13&amp;publication_year=2022&amp;author=Chi%2CY\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR10\">Bru\u00df, D. &amp; Macchiavello, C. Optimal eavesdropping in cryptography with three-dimensional quantum states. Phys. Rev. Lett. 88, 127901 (2002).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.88.127901\" data-track-item_id=\"10.1103\/PhysRevLett.88.127901\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.88.127901\" aria-label=\"Article reference 10\" data-doi=\"10.1103\/PhysRevLett.88.127901\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2002PhRvL..88l7901B\" aria-label=\"ADS reference 10\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 10\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Optimal%20eavesdropping%20in%20cryptography%20with%20three-dimensional%20quantum%20states&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.88.127901&amp;volume=88&amp;publication_year=2002&amp;author=Bru%C3%9F%2CD&amp;author=Macchiavello%2CC\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR11\">Pivoluska, M., Huber, M. &amp; Malik, M. Layered quantum key distribution. Phys. Rev. A 97, 032312 (2018).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.97.032312\" data-track-item_id=\"10.1103\/PhysRevA.97.032312\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.97.032312\" aria-label=\"Article reference 11\" data-doi=\"10.1103\/PhysRevA.97.032312\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2018PhRvA..97c2312P\" aria-label=\"ADS reference 11\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 11\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Layered%20quantum%20key%20distribution&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.97.032312&amp;volume=97&amp;publication_year=2018&amp;author=Pivoluska%2CM&amp;author=Huber%2CM&amp;author=Malik%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR12\">Doda, M. et al. Quantum key distribution overcoming extreme noise: simultaneous subspace coding using high-dimensional entanglement. Phys. Rev. Appl. 15, 034003 (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevApplied.15.034003\" data-track-item_id=\"10.1103\/PhysRevApplied.15.034003\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevApplied.15.034003\" aria-label=\"Article reference 12\" data-doi=\"10.1103\/PhysRevApplied.15.034003\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2021PhRvP..15c4003D\" aria-label=\"ADS reference 12\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 12\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20key%20distribution%20overcoming%20extreme%20noise%3A%20simultaneous%20subspace%20coding%20using%20high-dimensional%20entanglement&amp;journal=Phys.%20Rev.%20Appl.&amp;doi=10.1103%2FPhysRevApplied.15.034003&amp;volume=15&amp;publication_year=2021&amp;author=Doda%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR13\">Sit, A. et al. High-dimensional intracity quantum cryptography with structured photons. Optica 4, 1006\u20131010 (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1364\/OPTICA.4.001006\" data-track-item_id=\"10.1364\/OPTICA.4.001006\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1364%2FOPTICA.4.001006\" aria-label=\"Article reference 13\" data-doi=\"10.1364\/OPTICA.4.001006\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2017Optic...4.1006S\" aria-label=\"ADS reference 13\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 13\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=High-dimensional%20intracity%20quantum%20cryptography%20with%20structured%20photons&amp;journal=Optica&amp;doi=10.1364%2FOPTICA.4.001006&amp;volume=4&amp;pages=1006-1010&amp;publication_year=2017&amp;author=Sit%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR14\">Bulla, L. et al. Distribution of genuine high-dimensional entanglement over 10.2 km of noisy metropolitan atmosphere. Phys. Rev. A 107, L050402 (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.107.L050402\" data-track-item_id=\"10.1103\/PhysRevA.107.L050402\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.107.L050402\" aria-label=\"Article reference 14\" data-doi=\"10.1103\/PhysRevA.107.L050402\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2023PhRvA.107e0402B\" aria-label=\"ADS reference 14\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 14\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Distribution%20of%20genuine%20high-dimensional%20entanglement%20over%2010.2%20km%20of%20noisy%20metropolitan%20atmosphere&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.107.L050402&amp;volume=107&amp;publication_year=2023&amp;author=Bulla%2CL\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR15\">Lanyon, B. P. et al. Simplifying quantum logic using higher-dimensional Hilbert spaces. Nat. Phys. 5, 134\u2013140 (2009).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nphys1150\" data-track-item_id=\"10.1038\/nphys1150\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnphys1150\" aria-label=\"Article reference 15\" data-doi=\"10.1038\/nphys1150\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 15\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Simplifying%20quantum%20logic%20using%20higher-dimensional%20Hilbert%20spaces&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fnphys1150&amp;volume=5&amp;pages=134-140&amp;publication_year=2009&amp;author=Lanyon%2CBP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR16\">Wang, Y., Hu, Z., Sanders, B. C. &amp; Kais, S. Qudits and high-dimensional quantum computing. Front. Phys. 8, 479 (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.3389\/fphy.2020.589504\" data-track-item_id=\"10.3389\/fphy.2020.589504\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.3389%2Ffphy.2020.589504\" aria-label=\"Article reference 16\" data-doi=\"10.3389\/fphy.2020.589504\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 16\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Qudits%20and%20high-dimensional%20quantum%20computing&amp;journal=Front.%20Phys.&amp;doi=10.3389%2Ffphy.2020.589504&amp;volume=8&amp;publication_year=2020&amp;author=Wang%2CY&amp;author=Hu%2CZ&amp;author=Sanders%2CBC&amp;author=Kais%2CS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR17\">Ringbauer, M. et al. A universal qudit quantum processor with trapped ions. Nat. Phys. 18, 1053\u20131057 (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41567-022-01658-0\" data-track-item_id=\"10.1038\/s41567-022-01658-0\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41567-022-01658-0\" aria-label=\"Article reference 17\" data-doi=\"10.1038\/s41567-022-01658-0\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 17\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=A%20universal%20qudit%20quantum%20processor%20with%20trapped%20ions&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fs41567-022-01658-0&amp;volume=18&amp;pages=1053-1057&amp;publication_year=2022&amp;author=Ringbauer%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR18\">Hrmo, P. et al. Native qudit entanglement in a trapped ion quantum processor. Nat. Commun. 14, 2242 (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41467-023-37375-2\" data-track-item_id=\"10.1038\/s41467-023-37375-2\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41467-023-37375-2\" aria-label=\"Article reference 18\" data-doi=\"10.1038\/s41467-023-37375-2\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2023NatCo..14.2242H\" aria-label=\"ADS reference 18\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 18\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Native%20qudit%20entanglement%20in%20a%20trapped%20ion%20quantum%20processor&amp;journal=Nat.%20Commun.&amp;doi=10.1038%2Fs41467-023-37375-2&amp;volume=14&amp;publication_year=2023&amp;author=Hrmo%2CP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR19\">Gao, X., Appel, P., Friis, N., Ringbauer, M. &amp; Huber, M. On the role of entanglement in qudit\u2013based circuit compression. Quantum 7, 1141 (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.22331\/q-2023-10-16-1141\" data-track-item_id=\"10.22331\/q-2023-10-16-1141\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.22331%2Fq-2023-10-16-1141\" aria-label=\"Article reference 19\" data-doi=\"10.22331\/q-2023-10-16-1141\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 19\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=On%20the%20role%20of%20entanglement%20in%20qudit%E2%80%93based%20circuit%20compression&amp;journal=Quantum&amp;doi=10.22331%2Fq-2023-10-16-1141&amp;volume=7&amp;publication_year=2023&amp;author=Gao%2CX&amp;author=Appel%2CP&amp;author=Friis%2CN&amp;author=Ringbauer%2CM&amp;author=Huber%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR20\">Kiktenko, E. O., Nikolaeva, A. S., Xu, P., Shlyapnikov, G. V. &amp; Fedorov, A. K. Scalable quantum computing with qudits on a graph. Phys. Rev. A 101, 022304 (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.101.022304\" data-track-item_id=\"10.1103\/PhysRevA.101.022304\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.101.022304\" aria-label=\"Article reference 20\" data-doi=\"10.1103\/PhysRevA.101.022304\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2020PhRvA.101b2304K\" aria-label=\"ADS reference 20\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 20\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Scalable%20quantum%20computing%20with%20qudits%20on%20a%20graph&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.101.022304&amp;volume=101&amp;publication_year=2020&amp;author=Kiktenko%2CEO&amp;author=Nikolaeva%2CAS&amp;author=Xu%2CP&amp;author=Shlyapnikov%2CGV&amp;author=Fedorov%2CAK\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR21\">Nikolaeva, A. S., Kiktenko, E. O. &amp; Fedorov, A. K. Efficient realization of quantum algorithms with qudits. EPJ Quantum Technol. 11, 43 (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1140\/epjqt\/s40507-024-00250-0\" data-track-item_id=\"10.1140\/epjqt\/s40507-024-00250-0\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1140%2Fepjqt%2Fs40507-024-00250-0\" aria-label=\"Article reference 21\" data-doi=\"10.1140\/epjqt\/s40507-024-00250-0\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2024EPJQT..11...43N\" aria-label=\"ADS reference 21\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 21\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Efficient%20realization%20of%20quantum%20algorithms%20with%20qudits&amp;journal=EPJ%20Quantum%20Technol.&amp;doi=10.1140%2Fepjqt%2Fs40507-024-00250-0&amp;volume=11&amp;publication_year=2024&amp;author=Nikolaeva%2CAS&amp;author=Kiktenko%2CEO&amp;author=Fedorov%2CAK\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR22\">Gao, X., Erhard, M., Zeilinger, A. &amp; Krenn, M. Computer-inspired concept for high-dimensional multipartite quantum gates. Phys. Rev. Lett. 125, 050501 (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.125.050501\" data-track-item_id=\"10.1103\/PhysRevLett.125.050501\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.125.050501\" aria-label=\"Article reference 22\" data-doi=\"10.1103\/PhysRevLett.125.050501\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2020PhRvL.125e0501G\" aria-label=\"ADS reference 22\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=4131285\" aria-label=\"MathSciNet reference 22\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 22\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Computer-inspired%20concept%20for%20high-dimensional%20multipartite%20quantum%20gates&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.125.050501&amp;volume=125&amp;publication_year=2020&amp;author=Gao%2CX&amp;author=Erhard%2CM&amp;author=Zeilinger%2CA&amp;author=Krenn%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR23\">Babazadeh, A. et al. High-dimensional single-photon quantum gates: concepts and experiments. Phys. Rev. Lett. 119, 180510 (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.119.180510\" data-track-item_id=\"10.1103\/PhysRevLett.119.180510\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.119.180510\" aria-label=\"Article reference 23\" data-doi=\"10.1103\/PhysRevLett.119.180510\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2017PhRvL.119r0510B\" aria-label=\"ADS reference 23\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 23\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=High-dimensional%20single-photon%20quantum%20gates%3A%20concepts%20and%20experiments&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.119.180510&amp;volume=119&amp;publication_year=2017&amp;author=Babazadeh%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR24\">Brandt, F. et al. High-dimensional quantum gates using full\u2013field spatial modes of photons. Optica 7, 98\u2013107 (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1364\/OPTICA.375875\" data-track-item_id=\"10.1364\/OPTICA.375875\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1364%2FOPTICA.375875\" aria-label=\"Article reference 24\" data-doi=\"10.1364\/OPTICA.375875\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2020Optic...7...98B\" aria-label=\"ADS reference 24\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 24\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=High-dimensional%20quantum%20gates%20using%20full%E2%80%93field%20spatial%20modes%20of%20photons&amp;journal=Optica&amp;doi=10.1364%2FOPTICA.375875&amp;volume=7&amp;pages=98-107&amp;publication_year=2020&amp;author=Brandt%2CF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR25\">Nielsen, M. A. and Chuang, I. L. Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge Univ. Press, 2010).<\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR26\">Allen, L., Beijersbergen, M. W., Spreeuw, R. C. &amp; Woerdman, J. P. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys. Rev. A 45, 8185\u20138189 (1992).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.45.8185\" data-track-item_id=\"10.1103\/PhysRevA.45.8185\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.45.8185\" aria-label=\"Article reference 26\" data-doi=\"10.1103\/PhysRevA.45.8185\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=1992PhRvA..45.8185A\" aria-label=\"ADS reference 26\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 26\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Orbital%20angular%20momentum%20of%20light%20and%20the%20transformation%20of%20Laguerre-Gaussian%20laser%20modes&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.45.8185&amp;volume=45&amp;pages=8185-8189&amp;publication_year=1992&amp;author=Allen%2CL&amp;author=Beijersbergen%2CMW&amp;author=Spreeuw%2CRC&amp;author=Woerdman%2CJP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR27\">Krenn, M., Malik, M., Erhard, M. &amp; Zeilinger, A. Orbital angular momentum of photons and the entanglement of Laguerre-Gaussian modes. Phil. Trans. R. Soc. A 375, 20150442 (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1098\/rsta.2015.0442\" data-track-item_id=\"10.1098\/rsta.2015.0442\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1098%2Frsta.2015.0442\" aria-label=\"Article reference 27\" data-doi=\"10.1098\/rsta.2015.0442\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2017RSPTA.37550442K\" aria-label=\"ADS reference 27\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=3604852\" aria-label=\"MathSciNet reference 27\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 27\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Orbital%20angular%20momentum%20of%20photons%20and%20the%20entanglement%20of%20Laguerre-Gaussian%20modes&amp;journal=Phil.%20Trans.%20R.%20Soc.%20A&amp;doi=10.1098%2Frsta.2015.0442&amp;volume=375&amp;publication_year=2017&amp;author=Krenn%2CM&amp;author=Malik%2CM&amp;author=Erhard%2CM&amp;author=Zeilinger%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR28\">Barenco, A. et al. Elementary gates for quantum computation. Phys. Rev. A 52, 3457\u20133467 (1995).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.52.3457\" data-track-item_id=\"10.1103\/PhysRevA.52.3457\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.52.3457\" aria-label=\"Article reference 28\" data-doi=\"10.1103\/PhysRevA.52.3457\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=1995PhRvA..52.3457B\" aria-label=\"ADS reference 28\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 28\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Elementary%20gates%20for%20quantum%20computation&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.52.3457&amp;volume=52&amp;pages=3457-3467&amp;publication_year=1995&amp;author=Barenco%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR29\">O\u2019Brien, J. L., Pryde, G. J., White, A. G., Ralph, T. C. &amp; Branning, D. Demonstration of an all-optical quantum controlled-NOT gate. Nature 426, 264\u2013267 (2003).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nature02054\" data-track-item_id=\"10.1038\/nature02054\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnature02054\" aria-label=\"Article reference 29\" data-doi=\"10.1038\/nature02054\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2003Natur.426..264O\" aria-label=\"ADS reference 29\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 29\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Demonstration%20of%20an%20all-optical%20quantum%20controlled-NOT%20gate&amp;journal=Nature&amp;doi=10.1038%2Fnature02054&amp;volume=426&amp;pages=264-267&amp;publication_year=2003&amp;author=O%E2%80%99Brien%2CJL&amp;author=Pryde%2CGJ&amp;author=White%2CAG&amp;author=Ralph%2CTC&amp;author=Branning%2CD\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR30\">Pittman, T. B., Jacobs, B. C. &amp; Franson, J. D. Demonstration of nondeterministic quantum logic operations using linear optical elements. Phys. Rev. Lett. 88, 257902 (2002).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.88.257902\" data-track-item_id=\"10.1103\/PhysRevLett.88.257902\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.88.257902\" aria-label=\"Article reference 30\" data-doi=\"10.1103\/PhysRevLett.88.257902\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2002PhRvL..88y7902P\" aria-label=\"ADS reference 30\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 30\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Demonstration%20of%20nondeterministic%20quantum%20logic%20operations%20using%20linear%20optical%20elements&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.88.257902&amp;volume=88&amp;publication_year=2002&amp;author=Pittman%2CTB&amp;author=Jacobs%2CBC&amp;author=Franson%2CJD\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR31\">Langford, N. K. et al. Demonstration of a simple entangling optical gate and its use in Bell-state analysis. Phys. Rev. Lett. 95, 210504 (2005).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.95.210504\" data-track-item_id=\"10.1103\/PhysRevLett.95.210504\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.95.210504\" aria-label=\"Article reference 31\" data-doi=\"10.1103\/PhysRevLett.95.210504\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2005PhRvL..95u0504L\" aria-label=\"ADS reference 31\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 31\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Demonstration%20of%20a%20simple%20entangling%20optical%20gate%20and%20its%20use%20in%20Bell-state%20analysis&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.95.210504&amp;volume=95&amp;publication_year=2005&amp;author=Langford%2CNK\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR32\">Okamoto, R., Hofmann, H. F., Takeuchi, S. &amp; Sasaki, K. Demonstration of an optical quantum controlled-NOT gate without path interference. Phys. Rev. Lett. 95, 210506 (2005).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.95.210506\" data-track-item_id=\"10.1103\/PhysRevLett.95.210506\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.95.210506\" aria-label=\"Article reference 32\" data-doi=\"10.1103\/PhysRevLett.95.210506\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2005PhRvL..95u0506O\" aria-label=\"ADS reference 32\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 32\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Demonstration%20of%20an%20optical%20quantum%20controlled-NOT%20gate%20without%20path%20interference&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.95.210506&amp;volume=95&amp;publication_year=2005&amp;author=Okamoto%2CR&amp;author=Hofmann%2CHF&amp;author=Takeuchi%2CS&amp;author=Sasaki%2CK\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR33\">Gasparoni, S., Pan, J.-W., Walther, P., Rudolph, T. &amp; Zeilinger, A. Realization of a photonic controlled\u2013NOT gate sufficient for quantum computation. Phys. Rev. Lett. 93, 020504 (2004).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.93.020504\" data-track-item_id=\"10.1103\/PhysRevLett.93.020504\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.93.020504\" aria-label=\"Article reference 33\" data-doi=\"10.1103\/PhysRevLett.93.020504\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2004PhRvL..93b0504G\" aria-label=\"ADS reference 33\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 33\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Realization%20of%20a%20photonic%20controlled%E2%80%93NOT%20gate%20sufficient%20for%20quantum%20computation&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.93.020504&amp;volume=93&amp;publication_year=2004&amp;author=Gasparoni%2CS&amp;author=Pan%2CJ-W&amp;author=Walther%2CP&amp;author=Rudolph%2CT&amp;author=Zeilinger%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR34\">Zhao, Z. et al. Experimental demonstration of a nondestructive controlled-not quantum gate for two independent photon qubits. Phys. Rev. Lett. 94, 030501 (2005).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.94.030501\" data-track-item_id=\"10.1103\/PhysRevLett.94.030501\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.94.030501\" aria-label=\"Article reference 34\" data-doi=\"10.1103\/PhysRevLett.94.030501\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2005PhRvL..94c0501Z\" aria-label=\"ADS reference 34\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 34\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Experimental%20demonstration%20of%20a%20nondestructive%20controlled-not%20quantum%20gate%20for%20two%20independent%20photon%20qubits&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.94.030501&amp;volume=94&amp;publication_year=2005&amp;author=Zhao%2CZ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR35\">Huang, Y.-F., Ren, X.-F., Zhang, Y.-S., Duan, L.-M. &amp; Guo, G.-C. Experimental teleportation of a quantum controlled-NOT gate. Phys. Rev. Lett. 93, 240501 (2004).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.93.240501\" data-track-item_id=\"10.1103\/PhysRevLett.93.240501\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.93.240501\" aria-label=\"Article reference 35\" data-doi=\"10.1103\/PhysRevLett.93.240501\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2004PhRvL..93x0501H\" aria-label=\"ADS reference 35\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 35\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Experimental%20teleportation%20of%20a%20quantum%20controlled-NOT%20gate&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.93.240501&amp;volume=93&amp;publication_year=2004&amp;author=Huang%2CY-F&amp;author=Ren%2CX-F&amp;author=Zhang%2CY-S&amp;author=Duan%2CL-M&amp;author=Guo%2CG-C\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR36\">Zeuner, J. et al. Integrated-optics heralded controlled-NOT gate for polarization-encoded qubits. npj Quantum Inf. 4, 13 (2018).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41534-018-0068-0\" data-track-item_id=\"10.1038\/s41534-018-0068-0\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41534-018-0068-0\" aria-label=\"Article reference 36\" data-doi=\"10.1038\/s41534-018-0068-0\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2018npjQI...4...13Z\" aria-label=\"ADS reference 36\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 36\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Integrated-optics%20heralded%20controlled-NOT%20gate%20for%20polarization-encoded%20qubits&amp;journal=npj%20Quantum%20Inf.&amp;doi=10.1038%2Fs41534-018-0068-0&amp;volume=4&amp;publication_year=2018&amp;author=Zeuner%2CJ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR37\">Bao, X.-H. et al. Optical nondestructive controlled-NOT gate without using entangled photons. Phys. Rev. Lett. 98, 170502 (2007).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.98.170502\" data-track-item_id=\"10.1103\/PhysRevLett.98.170502\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.98.170502\" aria-label=\"Article reference 37\" data-doi=\"10.1103\/PhysRevLett.98.170502\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2007PhRvL..98q0502B\" aria-label=\"ADS reference 37\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 37\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Optical%20nondestructive%20controlled-NOT%20gate%20without%20using%20entangled%20photons&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.98.170502&amp;volume=98&amp;publication_year=2007&amp;author=Bao%2CX-H\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR38\">Li, J.-P. et al. Heralded nondestructive quantum entangling gate with single-photon sources. Phys. Rev. Lett. 126, 140501 (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.126.140501\" data-track-item_id=\"10.1103\/PhysRevLett.126.140501\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.126.140501\" aria-label=\"Article reference 38\" data-doi=\"10.1103\/PhysRevLett.126.140501\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2021PhRvL.126n0501L\" aria-label=\"ADS reference 38\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 38\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Heralded%20nondestructive%20quantum%20entangling%20gate%20with%20single-photon%20sources&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.126.140501&amp;volume=126&amp;publication_year=2021&amp;author=Li%2CJ-P\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR39\">Mair, A., Vaziri, A., Weihs, G. &amp; Zeilinger, A. Entanglement of the orbital angular momentum states of photons. Nature 412, 313\u2013316 (2001).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/35085529\" data-track-item_id=\"10.1038\/35085529\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2F35085529\" aria-label=\"Article reference 39\" data-doi=\"10.1038\/35085529\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2001Natur.412..313M\" aria-label=\"ADS reference 39\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 39\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Entanglement%20of%20the%20orbital%20angular%20momentum%20states%20of%20photons&amp;journal=Nature&amp;doi=10.1038%2F35085529&amp;volume=412&amp;pages=313-316&amp;publication_year=2001&amp;author=Mair%2CA&amp;author=Vaziri%2CA&amp;author=Weihs%2CG&amp;author=Zeilinger%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR40\">Wang, X.-L. et al. 18-qubit entanglement with six photons\u2019 three degrees of freedom. Phys. Rev. Lett. 120, 260502 (2018).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.120.260502\" data-track-item_id=\"10.1103\/PhysRevLett.120.260502\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.120.260502\" aria-label=\"Article reference 40\" data-doi=\"10.1103\/PhysRevLett.120.260502\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2018PhRvL.120z0502W\" aria-label=\"ADS reference 40\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 40\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=18-qubit%20entanglement%20with%20six%20photons%E2%80%99%20three%20degrees%20of%20freedom&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.120.260502&amp;volume=120&amp;publication_year=2018&amp;author=Wang%2CX-L\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR41\">Zhang, W., Qi, Q., Zhou, J. &amp; Chen, L. Mimicking Faraday rotation to sort the orbital angular momentum of light. Phys. Rev. Lett. 112, 153601 (2014).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.112.153601\" data-track-item_id=\"10.1103\/PhysRevLett.112.153601\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.112.153601\" aria-label=\"Article reference 41\" data-doi=\"10.1103\/PhysRevLett.112.153601\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2014PhRvL.112o3601Z\" aria-label=\"ADS reference 41\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 41\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Mimicking%20Faraday%20rotation%20to%20sort%20the%20orbital%20angular%20momentum%20of%20light&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.112.153601&amp;volume=112&amp;publication_year=2014&amp;author=Zhang%2CW&amp;author=Qi%2CQ&amp;author=Zhou%2CJ&amp;author=Chen%2CL\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR42\">Marrucci, L., Manzo, C. &amp; Paparo, D. Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media. Phys. Rev. Lett. 96, 163905 (2006).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.96.163905\" data-track-item_id=\"10.1103\/PhysRevLett.96.163905\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.96.163905\" aria-label=\"Article reference 42\" data-doi=\"10.1103\/PhysRevLett.96.163905\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2006PhRvL..96p3905M\" aria-label=\"ADS reference 42\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 42\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Optical%20spin-to-orbital%20angular%20momentum%20conversion%20in%20inhomogeneous%20anisotropic%20media&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.96.163905&amp;volume=96&amp;publication_year=2006&amp;author=Marrucci%2CL&amp;author=Manzo%2CC&amp;author=Paparo%2CD\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR43\">Agnew, M., Leach, J., McLaren, M., Roux, F. S. &amp; Boyd, R. W. Tomography of the quantum state of photons entangled in high dimensions. Phys. Rev. A 84, 062101 (2011).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.84.062101\" data-track-item_id=\"10.1103\/PhysRevA.84.062101\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.84.062101\" aria-label=\"Article reference 43\" data-doi=\"10.1103\/PhysRevA.84.062101\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2011PhRvA..84f2101A\" aria-label=\"ADS reference 43\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 43\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Tomography%20of%20the%20quantum%20state%20of%20photons%20entangled%20in%20high%20dimensions&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.84.062101&amp;volume=84&amp;publication_year=2011&amp;author=Agnew%2CM&amp;author=Leach%2CJ&amp;author=McLaren%2CM&amp;author=Roux%2CFS&amp;author=Boyd%2CRW\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR44\">Wu, S., Huang, W., Yang, P., Liu, S. &amp; Chen, L. Arbitrary phase-locking in Mach\u2013Zehnder interferometer. Opt. Commun. 442, 148\u2013151 (2019).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1016\/j.optcom.2019.03.031\" data-track-item_id=\"10.1016\/j.optcom.2019.03.031\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1016%2Fj.optcom.2019.03.031\" aria-label=\"Article reference 44\" data-doi=\"10.1016\/j.optcom.2019.03.031\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2019OptCo.442..148W\" aria-label=\"ADS reference 44\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 44\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Arbitrary%20phase-locking%20in%20Mach%E2%80%93Zehnder%20interferometer&amp;journal=Opt.%20Commun.&amp;doi=10.1016%2Fj.optcom.2019.03.031&amp;volume=442&amp;pages=148-151&amp;publication_year=2019&amp;author=Wu%2CS&amp;author=Huang%2CW&amp;author=Yang%2CP&amp;author=Liu%2CS&amp;author=Chen%2CL\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR45\">Black, E. D. An introduction to Pound-Drever-Hall laser frequency stabilization. Am. J. Phys. 69, 79\u201387 (2001).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1119\/1.1286663\" data-track-item_id=\"10.1119\/1.1286663\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1119%2F1.1286663\" aria-label=\"Article reference 45\" data-doi=\"10.1119\/1.1286663\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2001AmJPh..69...79B\" aria-label=\"ADS reference 45\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 45\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=An%20introduction%20to%20Pound-Drever-Hall%20laser%20frequency%20stabilization&amp;journal=Am.%20J.%20Phys.&amp;doi=10.1119%2F1.1286663&amp;volume=69&amp;pages=79-87&amp;publication_year=2001&amp;author=Black%2CED\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR46\">Wan, P. et al. Postselection-free cavity enhanced narrow band orbital angular momentum entangled photon source. Phys. Rev. Lett. 134, 053801 (2025).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.134.053801\" data-track-item_id=\"10.1103\/PhysRevLett.134.053801\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.134.053801\" aria-label=\"Article reference 46\" data-doi=\"10.1103\/PhysRevLett.134.053801\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2025PhRvL.134e3801W\" aria-label=\"ADS reference 46\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 46\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Postselection-free%20cavity%20enhanced%20narrow%20band%20orbital%20angular%20momentum%20entangled%20photon%20source&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.134.053801&amp;volume=134&amp;publication_year=2025&amp;author=Wan%2CP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR47\">Hofmann, H. F. Complementary classical fidelities as an efficient criterion for the evaluation of experimentally realized quantum operations. Phys. Rev. Lett. 94, 160504 (2005).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.94.160504\" data-track-item_id=\"10.1103\/PhysRevLett.94.160504\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.94.160504\" aria-label=\"Article reference 47\" data-doi=\"10.1103\/PhysRevLett.94.160504\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2005PhRvL..94p0504H\" aria-label=\"ADS reference 47\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=2146467\" aria-label=\"MathSciNet reference 47\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 47\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Complementary%20classical%20fidelities%20as%20an%20efficient%20criterion%20for%20the%20evaluation%20of%20experimentally%20realized%20quantum%20operations&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.94.160504&amp;volume=94&amp;publication_year=2005&amp;author=Hofmann%2CHF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR48\">Chen, M. et al. High-dimensional two-photon quantum controlled phase-flip gate. Phys. Rev. Research 6, 033004 (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevResearch.6.033004\" data-track-item_id=\"10.1103\/PhysRevResearch.6.033004\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevResearch.6.033004\" aria-label=\"Article reference 48\" data-doi=\"10.1103\/PhysRevResearch.6.033004\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2024PhRvR...6c3004C\" aria-label=\"ADS reference 48\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 48\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=High-dimensional%20two-photon%20quantum%20controlled%20phase-flip%20gate&amp;journal=Phys.%20Rev.%20Research&amp;doi=10.1103%2FPhysRevResearch.6.033004&amp;volume=6&amp;publication_year=2024&amp;author=Chen%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR49\">Jeff Kimble, H. The quantum internet. Nature 453, 1023\u20131030 (2008).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nature07127\" data-track-item_id=\"10.1038\/nature07127\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnature07127\" aria-label=\"Article reference 49\" data-doi=\"10.1038\/nature07127\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 49\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=The%20quantum%20internet&amp;journal=Nature&amp;doi=10.1038%2Fnature07127&amp;volume=453&amp;pages=1023-1030&amp;publication_year=2008&amp;author=Jeff%20Kimble%2CH\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR50\">Vitelli, C. et al. Joining the quantum state of two photons into one. Nat. Photon. 7, 521\u2013526 (2013).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nphoton.2013.107\" data-track-item_id=\"10.1038\/nphoton.2013.107\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnphoton.2013.107\" aria-label=\"Article reference 50\" data-doi=\"10.1038\/nphoton.2013.107\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2013NaPho...7..521V\" aria-label=\"ADS reference 50\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 50\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Joining%20the%20quantum%20state%20of%20two%20photons%20into%20one&amp;journal=Nat.%20Photon.&amp;doi=10.1038%2Fnphoton.2013.107&amp;volume=7&amp;pages=521-526&amp;publication_year=2013&amp;author=Vitelli%2CC\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR51\">Gao, X., Krenn, M., Kysela, J. &amp; Zeilinger, A. Arbitrary d-dimensional Pauli X gates of a flying qudit. Phys. Rev. A 99, 023825 (2019).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.99.023825\" data-track-item_id=\"10.1103\/PhysRevA.99.023825\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.99.023825\" aria-label=\"Article reference 51\" data-doi=\"10.1103\/PhysRevA.99.023825\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2019PhRvA..99b3825G\" aria-label=\"ADS reference 51\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 51\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Arbitrary%20d-dimensional%20Pauli%20X%20gates%20of%20a%20flying%20qudit&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.99.023825&amp;volume=99&amp;publication_year=2019&amp;author=Gao%2CX&amp;author=Krenn%2CM&amp;author=Kysela%2CJ&amp;author=Zeilinger%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR52\">Wang, X., Sanders, B. C. &amp; Berry, D. W. Entangling power and operator entanglement in qudit systems. Phys. Rev. A 67, 042323 (2003).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.67.042323\" data-track-item_id=\"10.1103\/PhysRevA.67.042323\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.67.042323\" aria-label=\"Article reference 52\" data-doi=\"10.1103\/PhysRevA.67.042323\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2003PhRvA..67d2323W\" aria-label=\"ADS reference 52\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 52\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Entangling%20power%20and%20operator%20entanglement%20in%20qudit%20systems&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.67.042323&amp;volume=67&amp;publication_year=2003&amp;author=Wang%2CX&amp;author=Sanders%2CBC&amp;author=Berry%2CDW\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR53\">Barreiro, J. T., Wei, T.-C. &amp; Kwiat, P. G. Beating the channel capacity limit for linear photonic superdense coding. Nat. Phys. 4, 282\u2013286 (2008).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nphys919\" data-track-item_id=\"10.1038\/nphys919\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnphys919\" aria-label=\"Article reference 53\" data-doi=\"10.1038\/nphys919\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 53\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Beating%20the%20channel%20capacity%20limit%20for%20linear%20photonic%20superdense%20coding&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fnphys919&amp;volume=4&amp;pages=282-286&amp;publication_year=2008&amp;author=Barreiro%2CJT&amp;author=Wei%2CT-C&amp;author=Kwiat%2CPG\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR54\">Wang, X.-L. et al. Quantum teleportation of multiple degrees of freedom of a single photon. Nature 518, 516\u2013519 (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nature14246\" data-track-item_id=\"10.1038\/nature14246\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnature14246\" aria-label=\"Article reference 54\" data-doi=\"10.1038\/nature14246\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2015Natur.518..516W\" aria-label=\"ADS reference 54\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 54\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20teleportation%20of%20multiple%20degrees%20of%20freedom%20of%20a%20single%20photon&amp;journal=Nature&amp;doi=10.1038%2Fnature14246&amp;volume=518&amp;pages=516-519&amp;publication_year=2015&amp;author=Wang%2CX-L\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR55\">Williams, B. P., Sadlier, R. J. &amp; Humble, T. S. Superdense coding over optical fiber links with complete Bell-state measurements. Phys. Rev. Lett. 118, 050501 (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.118.050501\" data-track-item_id=\"10.1103\/PhysRevLett.118.050501\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.118.050501\" aria-label=\"Article reference 55\" data-doi=\"10.1103\/PhysRevLett.118.050501\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2017PhRvL.118e0501W\" aria-label=\"ADS reference 55\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 55\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Superdense%20coding%20over%20optical%20fiber%20links%20with%20complete%20Bell-state%20measurements&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.118.050501&amp;volume=118&amp;publication_year=2017&amp;author=Williams%2CBP&amp;author=Sadlier%2CRJ&amp;author=Humble%2CTS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR56\">Luo, Y.-H. et al. Quantum teleportation in high dimensions. Phys. Rev. Lett. 123, 070505 (2019).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.123.070505\" data-track-item_id=\"10.1103\/PhysRevLett.123.070505\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.123.070505\" aria-label=\"Article reference 56\" data-doi=\"10.1103\/PhysRevLett.123.070505\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2019PhRvL.123g0505L\" aria-label=\"ADS reference 56\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 56\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20teleportation%20in%20high%20dimensions&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.123.070505&amp;volume=123&amp;publication_year=2019&amp;author=Luo%2CY-H\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR57\">Reimer, C. et al. High-dimensional one-way quantum processing implemented on d-level cluster states. Nat. Phys. 15, 148\u2013153 (2019).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41567-018-0347-x\" data-track-item_id=\"10.1038\/s41567-018-0347-x\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41567-018-0347-x\" aria-label=\"Article reference 57\" data-doi=\"10.1038\/s41567-018-0347-x\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 57\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=High-dimensional%20one-way%20quantum%20processing%20implemented%20on%20d-level%20cluster%20states&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fs41567-018-0347-x&amp;volume=15&amp;pages=148-153&amp;publication_year=2019&amp;author=Reimer%2CC\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR58\">Hu, X.-M. et al. Experimental high-dimensional quantum teleportation. Phys. Rev. Lett. 125, 230501 (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.125.230501\" data-track-item_id=\"10.1103\/PhysRevLett.125.230501\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.125.230501\" aria-label=\"Article reference 58\" data-doi=\"10.1103\/PhysRevLett.125.230501\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2020PhRvL.125w0501H\" aria-label=\"ADS reference 58\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 58\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Experimental%20high-dimensional%20quantum%20teleportation&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.125.230501&amp;volume=125&amp;publication_year=2020&amp;author=Hu%2CX-M\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR59\">Terhal, B. M. Quantum error correction for quantum memories. Rev. Mod. Phys. 87, 307\u2013346 (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/RevModPhys.87.307\" data-track-item_id=\"10.1103\/RevModPhys.87.307\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FRevModPhys.87.307\" aria-label=\"Article reference 59\" data-doi=\"10.1103\/RevModPhys.87.307\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2015RvMP...87..307T\" aria-label=\"ADS reference 59\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=3403261\" aria-label=\"MathSciNet reference 59\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 59\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20error%20correction%20for%20quantum%20memories&amp;journal=Rev.%20Mod.%20Phys.&amp;doi=10.1103%2FRevModPhys.87.307&amp;volume=87&amp;pages=307-346&amp;publication_year=2015&amp;author=Terhal%2CBM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR60\">Bocharov, A., Roetteler, M. &amp; Svore, K. M. Factoring with qutrits: Shor\u2019s algorithm on ternary and metaplectic quantum architectures. Phys. Rev. A 96, 012306 (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.96.012306\" data-track-item_id=\"10.1103\/PhysRevA.96.012306\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.96.012306\" aria-label=\"Article reference 60\" data-doi=\"10.1103\/PhysRevA.96.012306\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2017PhRvA..96a2306B\" aria-label=\"ADS reference 60\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 60\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Factoring%20with%20qutrits%3A%20Shor%E2%80%99s%20algorithm%20on%20ternary%20and%20metaplectic%20quantum%20architectures&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.96.012306&amp;volume=96&amp;publication_year=2017&amp;author=Bocharov%2CA&amp;author=Roetteler%2CM&amp;author=Svore%2CKM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR61\">Miao, K. C. et al. Overcoming leakage in quantum error correction. Nat. Phys. 19, 1780\u20131786 (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41567-023-02226-w\" data-track-item_id=\"10.1038\/s41567-023-02226-w\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41567-023-02226-w\" aria-label=\"Article reference 61\" data-doi=\"10.1038\/s41567-023-02226-w\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 61\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Overcoming%20leakage%20in%20quantum%20error%20correction&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fs41567-023-02226-w&amp;volume=19&amp;pages=1780-1786&amp;publication_year=2023&amp;author=Miao%2CKC\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR62\">Muthukrishnan, A. &amp; Stroud, C. R. Multi-valued logic gates for quantum computation. Phys. Rev. A 62, 052309 (2000).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.62.052309\" data-track-item_id=\"10.1103\/PhysRevA.62.052309\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.62.052309\" aria-label=\"Article reference 62\" data-doi=\"10.1103\/PhysRevA.62.052309\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2000PhRvA..62e2309M\" aria-label=\"ADS reference 62\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=1792931\" aria-label=\"MathSciNet reference 62\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 62\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Multi-valued%20logic%20gates%20for%20quantum%20computation&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.62.052309&amp;volume=62&amp;publication_year=2000&amp;author=Muthukrishnan%2CA&amp;author=Stroud%2CCR\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR63\">Grover, L. K. Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79, 325\u2013328 (1997).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.79.325\" data-track-item_id=\"10.1103\/PhysRevLett.79.325\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.79.325\" aria-label=\"Article reference 63\" data-doi=\"10.1103\/PhysRevLett.79.325\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=1997PhRvL..79..325G\" aria-label=\"ADS reference 63\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 63\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20mechanics%20helps%20in%20searching%20for%20a%20needle%20in%20a%20haystack&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.79.325&amp;volume=79&amp;pages=325-328&amp;publication_year=1997&amp;author=Grover%2CLK\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR64\">Wang, X.-L. et al. Experimental ten-photon entanglement. Phys. Rev. Lett. 117, 210502 (2016).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.117.210502\" data-track-item_id=\"10.1103\/PhysRevLett.117.210502\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.117.210502\" aria-label=\"Article reference 64\" data-doi=\"10.1103\/PhysRevLett.117.210502\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2016PhRvL.117u0502W\" aria-label=\"ADS reference 64\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 64\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Experimental%20ten-photon%20entanglement&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.117.210502&amp;volume=117&amp;publication_year=2016&amp;author=Wang%2CX-L\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR65\">Zhong, H.-S. et al. 12-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion. Phys. Rev. Lett. 121, 250505 (2018).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.121.250505\" data-track-item_id=\"10.1103\/PhysRevLett.121.250505\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.121.250505\" aria-label=\"Article reference 65\" data-doi=\"10.1103\/PhysRevLett.121.250505\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2018PhRvL.121y0505Z\" aria-label=\"ADS reference 65\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 65\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=12-photon%20entanglement%20and%20scalable%20scattershot%20boson%20sampling%20with%20optimal%20entangled-photon%20pairs%20from%20parametric%20down-conversion&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.121.250505&amp;volume=121&amp;publication_year=2018&amp;author=Zhong%2CH-S\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR66\">Liu, Z. et al. Supporting data for heralded high-dimensional photon-photon quantum gate. Figshare <a href=\"https:\/\/doi.org\/10.6084\/m9.figshare.30946265\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.6084\/m9.figshare.30946265\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.6084\/m9.figshare.30946265<\/a> (2025).<\/p>\n","protected":false},"excerpt":{"rendered":"Vertesi, T., Pironio, S. &amp; Brunner, N. Closing the detection loophole in Bell experiments using qudits. Phys. Rev.&hellip;\n","protected":false},"author":2,"featured_media":468091,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[24],"tags":[23349,49,48,3673,314,3230,37833,5964,66],"class_list":["post-468090","post","type-post","status-publish","format-standard","has-post-thumbnail","category-physics","tag-applied-and-technical-physics","tag-ca","tag-canada","tag-general","tag-physics","tag-quantum-information","tag-quantum-optics","tag-quantum-physics","tag-science"],"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/posts\/468090","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/comments?post=468090"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/posts\/468090\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/media\/468091"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/media?parent=468090"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/categories?post=468090"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/tags?post=468090"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}