Bennett, C. H. & Brassard, G. Quantum cryptography: public key distribution and coin tossing. Theor. Comput. Sci. 560, 7–11 (2014).
Ekert, A. K. Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–663 (1991).
Gisin, N., Ribordy, G., Tittel, W. & Zbinden, H. Quantum cryptography. Rev. Mod. Phys. 74, 145–195 (2002).
Scarani, V. et al. The security of practical quantum key distribution. Rev. Mod. Phys. 81, 1301–1350 (2009).
Liao, S.-K. et al. Satellite-to-ground quantum key distribution. Nature 549, 43–47 (2017).
Liao, S.-K. et al. Satellite-relayed intercontinental quantum network. Phys. Rev. Lett. 120, 030501 (2018).
Yin, J. et al. Satellite-based entanglement distribution over 1,200 kilometers. Science 356, 1140–1144 (2017).
Yin, J. et al. Entanglement-based secure quantum cryptography over 1,120 kilometres. Nature 582, 501–505 (2020).
Yin, J. et al. Satellite-to-ground entanglement-based quantum key distribution. Phys. Rev. Lett. 119, 200501 (2017).
Ren, J.-G. et al. Ground-to-satellite quantum teleportation. Nature 549, 70–73 (2017).
Chen, Y.-A. et al. An integrated space-to-ground quantum communication network over 4,600 kilometres. Nature 589, 214–219 (2021).
Lu, C.-Y., Cao, Y., Peng, C.-Z. & Pan, J.-W. Micius quantum experiments in space. Rev. Mod. Phys. 94, 035001 (2022).
Xu, F., Ma, X., Zhang, Q., Lo, H.-K. & Pan, J.-W. Secure quantum key distribution with realistic devices. Rev. Mod. Phys. 92, 025002 (2020).
Lo, H.-K., Curty, M. & Qi, B. Measurement-device-independent quantum key distribution. Phys. Rev. Lett. 108, 130503 (2012).
Braunstein, S. L. & Pirandola, S. Side-channel-free quantum key distribution. Phys. Rev. Lett. 108, 130502 (2012).
Wang, X.-B. Beating the photon-number-splitting attack in practical quantum cryptography. Phys. Rev. Lett. 94, 230503 (2005).
Lo, H.-K., Ma, X. & Chen, K. Decoy state quantum key distribution. Phys. Rev. Lett. 94, 230504 (2005).
Lucamarini, M., Yuan, Z. L., Dynes, J. F. & Shields, A. J. Overcoming the rate-distance limit of quantum key distribution without quantum repeaters. Nature 557, 400–403 (2018).
Minder, M. et al. Experimental quantum key distribution beyond the repeaterless secret key capacity. Nat. Photon. 13, 334–338 (2019).
Wang, S. et al. Beating the fundamental rate-distance limit in a proof-of-principle quantum key distribution system. Phys. Rev. X 9, 021046 (2019).
Liu, Y. et al. Experimental twin-field quantum key distribution through sending or not sending. Phys. Rev. Lett. 123, 100505 (2019).
Zhong, X., Hu, J., Curty, M., Qian, L. & Lo, H.-K. Proof-of-principle experimental demonstration of twin-field type quantum key distribution. Phys. Rev. Lett. 123, 100506 (2019).
Fang, X.-T. et al. Implementation of quantum key distribution surpassing the linear rate-transmittance bound. Nat. Photon. 14, 422–425 (2020).
Chen, J.-P. et al. Sending-or-not-sending with independent lasers: secure twin-field quantum key distribution over 509 km. Phys. Rev. Lett. 124, 070501 (2020).
Liu, H. et al. Field test of twin-field quantum key distribution through sending-or-not-sending over 428 km. Phys. Rev. Lett. 126, 250502 (2021).
Chen, J.-P. et al. Twin-field quantum key distribution over a 511 km optical fibre linking two distant metropolitan areas. Nat. Photon. 15, 570–575 (2021).
Chen, J.-P. et al. Quantum key distribution over 658 km fiber with distributed vibration sensing. Phys. Rev. Lett. 128, 180502 (2022).
Pittaluga, M. et al. 600-km repeater-like quantum communications with dual-band stabilization. Nat. Photon. 15, 530–535 (2021).
Wang, S. et al. Twin-field quantum key distribution over 830-km fibre. Nat. Photon. 16, 154–161 (2022).
Liu, Y. et al. Experimental twin-field quantum key distribution over 1,000 km fiber distance. Phys. Rev. Lett. 130, 210801 (2023).
Zhou, L., Lin, J., Jing, Y. & Yuan, Z. Twin-field quantum key distribution without optical frequency dissemination. Nat. Commun. 14, 928 (2023).
Zhou, L. et al. Experimental quantum communication overcomes the rate-loss limit without global phase tracking. Phys. Rev. Lett. 130, 250801 (2023).
Li, W. et al. Twin-field quantum key distribution without phase locking. Phys. Rev. Lett. 130, 250802 (2023).
Chen, J.-P. et al. Twin-field quantum key distribution with local frequency reference. Phys. Rev. Lett. 132, 260802 (2024).
Pittaluga, M. et al. Long-distance coherent quantum communications in deployed telecom networks. Nature 640, 911–917 (2025).
Cao, Y. et al. Long-distance free-space measurement-device-independent quantum key distribution. Phys. Rev. Lett. 125, 260503 (2020).
Li, Y.-H. et al. Free-space and fiber-integrated measurement-device-independent quantum key distribution under high background noise. Phys. Rev. Lett. 131, 100802 (2023).
Pirandola, S., Laurenza, R., Ottaviani, C. & Banchi, L. Fundamental limits of repeaterless quantum communications. Nat. Commun. 8, 15043 (2017).
Bennett, C. H. et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895 (1993).
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, 5932–5935 (1998).
Cirac, J. I., Ekert, A. K., Huelga, S. F. & Macchiavello, C. Distributed quantum computation over noisy channels. Phys. Rev. A 59, 4249–4254 (1999).
Rideout, D. et al. Fundamental quantum optics experiments conceivable with satellites—reaching relativistic distances and velocities. Classical Quantum Gravity 29, 224011 (2012).
Wang, X.-B., Yu, Z.-W. & Hu, X.-L. Twin-field quantum key distribution with large misalignment error. Phys. Rev. A 98, 062323 (2018).
Fried, D. L. Optical resolution through a randomly inhomogeneous medium for very long and very short exposures. J. Opt. Soc. Am. 56, 1372–1379 (1966).
Jiang, C., Hu, X.-L., Xu, H., Yu, Z.-W. & Wang, X.-B. Zigzag approach to higher key rate of sending-or-not-sending twin field quantum key distribution with finite-key effects. New J. Phys. 22, 053048 (2020).
Li, Y. et al. Microsatellite-based real-time quantum key distribution. Nature 640, 47–54 (2025).
Du, H. et al. Twin-field quantum key distribution with optical injection locking and phase encoding on-chip. Optica 11, 1385–1390 (2024).
Guo, J. et al. Chip-based laser with 1-hertz integrated linewidth. Sci. Adv. 8, 9006 (2022).
Wei, K. et al. High-speed measurement-device-independent quantum key distribution with integrated silicon photonics. Phys. Rev. X 10, 031030 (2020).
Cao, L. et al. Chip-based measurement-device-independent quantum key distribution using integrated silicon photonic systems. Phys. Rev. Appl. 14, 011001 (2020).
Semenenko, H. et al. Chip-based measurement-device-independent quantum key distribution. Optica 7, 238–242 (2020).
You, L. et al. Superconducting nanowire single photon detection system for space applications. Opt. Express 26, 2965–2971 (2018).
Halder, M. et al. Entangling independent photons by time measurement. Nat. Phys. 3, 692–695 (2007).
Anderson, R., Bilger, H. R. & Stedman, G. E. ‘Sagnac’ effect: a century of Earth-rotated interferometers. Am. J. Phys. 62, 975–985 (1994).
Hu, X.-L., Jiang, C., Yu, Z.-W. & Wang, X.-B. Universal approach to sending-or-not-sending twin field quantum key distribution. Quantum Sci. Technol. 7, 045031 (2022).
Vitanov, A., Dupuis, F., Tomamichel, M. & Renner, R. Chain rules for smooth min-and max-entropies. IEEE Trans. Inf. Theory 59, 2603–2612 (2013).
Zhong, X., Wang, W., Qian, L. & Lo, H.-K. Proof-of-principle experimental demonstration of twin-field quantum key distribution over optical channels with asymmetric losses. npj Quantum Inf. 7, 8 (2021).
Li, Y.-H. Free-space twin-field quantum key distribution [data set]. Zenodo https://doi.org/10.5281/zenodo.19162195 (2026).
Li. H. InteractionFreePy. GitHub http://github.com/hwaipy/InteractionFreePy (2022).