Shor, P. W. Algorithms for quantum computation: discrete logarithms and factoring. In Proc. 35th Annual Symposium on Foundations of Computer Science 124–134 (IEEE, 1994).
Grover, L. K. A fast quantum mechanical algorithm for database search. In Proc. 28th Annual ACM Symposium on Theory of Computing 212–219 (ACM, 1996).
Bennett, C. H. & Brassard, G. Quantum cryptography: public key distribution and coin tossing. In Proc. IEEE International Conference on Computers, Systems and Signal Processing 175–179 (IEEE, 1984).
Ekert, A. K. Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991).
Giovannetti, V., Lloyd, S. & Maccone, L. Quantum-enhanced measurements: beating the standard quantum limit. Science 306, 1330–1336 (2004).
Giovannetti, V., Lloyd, S. & Maccone, L. Advances in quantum metrology. Nat. Photon. 5, 222–229 (2011).
Chen, Y.-A. et al. An integrated space-to-ground quantum communication network over 4,600 kilometres. Nature 589, 214–219 (2021).
Peev, M. et al. The SECOQC quantum key distribution network in Vienna. New J. Phys. 11, 075001 (2009).
Sasaki, M. et al. Field test of quantum key distribution in the Tokyo QKD network. Opt. Express 19, 10387–10409 (2011).
Simon, C. Towards a global quantum network. Nat. Photon. 11, 678–680 (2017).
Van Meter, R. & Devitt, S. J. The path to scalable distributed quantum computing. Computer 49, 31–42 (2016).
Broadbent, A., Fitzsimons, J. & Kashefi, E. Universal blind quantum computation. In 2009 50th Annual IEEE Symposium on Foundations of Computer Science 517–526 (IEEE, 2009).
Briegel, H.-J., Dür, W., Cirac, J. I. & Zoller, P. Quantum repeaters: the role of imperfect local operations in quantum communication. Phys. Rev. Lett. 81, 5932 (1998).
Duan, L.-M., Lukin, M., Cirac, J. I. & Zoller, P. Long-distance quantum communication with atomic ensembles and linear optics. Nature 414, 413–418 (2001).
Jacobs, B. C., Pittman, T. B. & Franson, J. D. Quantum relays and noise suppression using linear optics. Phys. Rev. A 66, 052307 (2002).
Waks, E., Zeevi, A. & Yamamoto, Y. Security of quantum key distribution with entangled photons against individual attacks. Phys. Rev. A 65, 052310 (2002).
de Riedmatten, H. et al. Long distance quantum teleportation in a quantum relay configuration. Phys. Rev. Lett. 92, 047904 (2004).
Collins, D., Gisin, N. & De Riedmatten, H. Quantum relays for long distance quantum cryptography. J. Mod. Opt. 52, 735–753 (2005).
Jing, B. et al. Entanglement of three quantum memories via interference of three single photons. Nat. Photon. 13, 210–213 (2019).
Yu, Y. et al. Entanglement of two quantum memories via fibres over dozens of kilometres. Nature 578, 240–245 (2020).
Pompili, M. et al. Realization of a multinode quantum network of remote solid-state qubits. Science 372, 259–264 (2021).
Hermans, S. et al. Qubit teleportation between non-neighbouring nodes in a quantum network. Nature 605, 663–668 (2022).
Liu, J.-L. et al. Creation of memory–memory entanglement in a metropolitan quantum network. Nature 629, 579–585 (2024).
Lucamarini, M., Yuan, Z., Dynes, J. & Shields, A. Overcoming the rate–distance limit of quantum key distribution without quantum repeaters. Nature 557, 400–403 (2018).
Ma, X., Zeng, P. & Zhou, H. Phase-matching quantum key distribution. Phys. Rev. X 8, 031043 (2018).
Hwang, W.-Y. Quantum key distribution with high loss: toward global secure communication. Phys. Rev. Lett. 91, 057901 (2003).
Lo, H.-K., Ma, X. & Chen, K. Decoy state quantum key distribution. Phys. Rev. Lett. 94, 230504 (2005).
Wang, X.-B. Beating the photon-number-splitting attack in practical quantum cryptography. Phys. Rev. Lett. 94, 230503 (2005).
Lo, H.-K. & Chau, H. F. Unconditional security of quantum key distribution over arbitrarily long distances. Science 283, 2050–2056 (1999).
Kurtsiefer, C., Mayer, S., Zarda, P. & Weinfurter, H. Stable solid-state source of single photons. Phys. Rev. Lett. 85, 290 (2000).
Aharonovich, I., Englund, D. & Toth, M. Solid-state single-photon emitters. Nat. Photon. 10, 631–641 (2016).
Keller, M., Lange, B., Hayasaka, K., Lange, W. & Walther, H. Continuous generation of single photons with controlled waveform in an ion-trap cavity system. Nature 431, 1075–1078 (2004).
Michler, P. et al. A quantum dot single-photon turnstile device. Science 290, 2282–2285 (2000).
Ding, X. et al. On-demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driven quantum dot in a micropillar. Phys. Rev. Lett. 116, 020401 (2016).
Ding, X. High-efficiency single-photon source above the loss-tolerant threshold for efficient linear optical quantum computing. Nat. Photon. 19, 387–391 (2025).
Chou, C. W., Polyakov, S. V., Kuzmich, A. & Kimble, H. J. Single-photon generation from stored excitation in an atomic ensemble. Phys. Rev. Lett. 92, 213601 (2004).
Ripka, F., Kübler, H., Löw, R. & Pfau, T. A room-temperature single-photon source based on strongly interacting Rydberg atoms. Science 362, 446–449 (2018).
Zeng, P., Wu, W. & Ma, X. Symmetry-protected privacy: beating the rate-distance linear bound over a noisy channel. Phys. Rev. Appl. 13, 064013 (2020).