Measurement-device-independent quantum key distribution of multiple degrees of freedom of a single photon

Abstract

Measurement-device-independent quantum key distribution (MDI-QKD) provides us a powerful approach to resist all attacks at detection side. Besides the unconditional security, people also seek for high key generation rate, but MDI-QKD has relatively low key generation rate. In this paper, we provide an efficient approach to increase the key generation rate of MDI-QKD by adopting multiple degrees of freedom (DOFs) of single photons to generate keys. Compared with other high-dimension MDI-QKD protocols encoding in one DOF, our protocol is more flexible, for our protocol generating keys in independent subsystems and the detection failure or error in a DOF not affecting the information encoding in other DOFs. Based on above features, our MDI-QKD protocol may have potential application in future quantum communication field.

Keywords

measurement-device-independent quantum key distribution / polarization / longitudinal-momentum / key generation rate

References

[1] C. H. Bennett and G. Brassard, in: Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India IEEE, New York, 175 (1984)

[2] A. K. Ekert, Quantum cryptography based on Bell’s theorem, Phys. Rev. Lett. 67(6), 661 (1991)

[3] H. K. Lo and H. F. Chau, Unconditional security of quantum key distribution over arbitrarily long distances, Science 283(5410), 2050 (1999)

[4] N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, Security of quantum key distribution using d-level systems, Phys. Rev. Lett. 88(12), 127902 (2002)

[5] D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, and H. Zbinden, Quantum key distribution over 67 km with a plug play system, New J. Phys. 4, 41 (2002)

[6] F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, Quantum key distribution using gaussian-modulated coherent states, Nature 421(6920), 238 (2003)

[7] H. K. Lo, H. F. Chau, and M. Ardehali, Efficient quantum key distribution scheme and a proof of its unconditional security, J. Cryptol. 18(2), 133 (2005)

[8] T. Schmitt-Manderbach, H. Weier, M. Fürst, R. Ursin, F. Tiefenbacher, T. Scheidl, J. Perdigues, Z. Sodnik, C. Kurtsiefer, J. G. Rarity, A. Zeilinger, and H. Weinfurter, Experimental demonstration of free-space decoy-state quantum key distribution over 144 km, Phys. Rev. Lett. 98(1), 010504 (2007)

[9] M. Koashi, Simple security proof of quantum key distribution based on complementarity, New J. Phys. 11(4), 045018 (2009)

[10] S. Wang, W. Chen, Z. Q. Yin, D. Y. He, C. Hui, P. L. Hao, G. J. Fan-Yuan, C. Wang, L. J. Zhang, J. Kuang, S. F. Liu, Z. Zhou, Y. G. Wang, G. C. Guo, and Z. F. Han, Practical gigahertz quantum key distribution robust against channel disturbance, Opt. Lett. 43(9), 2030 (2018)

[11] X. D. Wu, Y. J. Wang, H. Zhong, Q. Liao, and Y. Guo, Plug-and-play dual-phase-modulated continuous variable quantum key distribution with photon subtraction, Front. Phys. 14(4), 41501 (2019)

[12] S. Wang, D. Y. He, Z. Q. Yin, F. Y. Lu, C. H. Cui, W. Chen, Z. Zhou, G. C. Guo, and Z. F. Han, Beating the fundamental rate-distance limit in a proof-of-principle quantum key distribution system, Phys. Rev. X 9(2), 021046 (2019)

[13] F. H. Xu, X. F. Ma, Q. Zhang, H. K. Lo, and J. W. Pan, Secure quantum key distribution with realistic devices, Rev. Mod. Phys. 92(2), 025002 (2020)

[14] Y. Zhang and Q. Ni, Design and analysis of random multiple access quantum key distribution, Quant. Engineer. 2(1), e31 (2020)

[15] G. Chai, D. W. Li, Z. W. Cao, M. Zhang, P. Huang, and G. Zeng, Blind channel estimation for continuousvariable quantum key distribution, Quant. Engineer. 2(2), e37 (2020)

[16] M. J. He, R. Malaney, and J. Green, Multimode CV-QKD with non-Gaussian operations, Quant. Engineer. 2, e40 (2020)

[17] H. K. Lo, M. Curty, and K. Tamaki, Secure quantum key distribution, Nat. Photonics 8(8), 595 (2014)

[18] B. Qi, C. H. F. Fung, H. K. Lo, and X. F. Ma, Time-shift attack in practical quantum cryptosystems, Quantum Inf. Comput. 7, 73 (2007)

[19] Y. Zhao, C. H. F. Fung, B. Qi, C. Chen, and H. K. Lo, Quantum hacking: experimental demonstration of timeshift attack against practical quantum-keydistribution systems, Phys. Rev. A 78(4), 042333 (2008)

[20] N. Jain, C. Wittmann, L. Lydersen, C. Wiechers, D. Elser, C. Marquardt, V. Makarov, and G. Leuchs, Device calibration impacts security of quantum key distribution, Phys. Rev. Lett. 107(11), 110501 (2011)

[21] L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, Hacking commercial quantum cryptography systems by tailored bright illumination, Nat. Photonics 4(10), 686 (2010)

[22] H. W. Li, S. Wang, J. Z. Huang, W. Chen, Z. Q. Yin, F. Y. Li, Z. Zhou, D. Liu, Y. Zhang, G. C. Guo, W. S. Bao, and Z. F. Han, Attacking a practical quantum-key-distribution system with wavelength dependent beam-splitter and multiwavelength sources, Phys. Rev. A 84(6), 062308 (2011)

[23] J. Z. Huang, C. Weedbrook, Z. Q. Yin, S. Wang, H. W. Li, W. Chen, G. C. Guo, and Z. F. Han, Quantum hacking of a continuous-variable quantum-key distribution system using a wavelength attack, Phys. Rev. A 87(6), 062329 (2013)

[24] V. Makarov and J. Skaar, Faked states attack using detector efficiency mismatch on SARG04, phase-time, DPSK, and Ekert protocols, Quantum Inf. Comput. 8, 6 (2007)

[25] V. Makarov, A. Anisimov, and J. Skaar, Effects of detector efficiency mismatch on security of quantum cryptosystems, Phys. Rev. A 74(2), 022313 (2006)

[26] Y. Zhao, B. Qi, and H. K. Lo, Quantum key distribution with an unknown and untrusted source, Phys. Rev. A 77(5), 052327 (2008)

[27] X. Peng, H. Jiang, B. J. Xu, X. F. Ma, and H. Guo, Experimental quantum-key distribution with an untrusted source, Opt. Lett. 33(18), 2077 (2008)

[28] G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, Limitations on practical quantum cryptography, Phys. Rev. Lett. 85(6), 1330 (2000)

[29] W. Y. Hwang, Quantum key distribution with high loss: Toward global secure communication, Phys. Rev. Lett. 91(5), 057901 (2003)

[30] H. K. Lo, X. F. Ma, and K. Chen, Decoy state quantum key distribution, Phys. Rev. Lett. 94(23), 230504 (2005)

[31] X. B. Wang, Beating the photon-number-splitting attack in practical quantum cryptography, Phys. Rev. Lett. 94(23), 230503 (2005)

[32] X. F. Ma, B. Qi, Y. Zhao, and H. K. Lo, Practical decoy state for quantum key distribution, Phys. Rev. A 72(1), 012326 (2005)

[33] A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, Device-independent security of quantum cryptography against collective attacks, Phys. Rev. Lett. 98(23), 230501 (2007)

[34] S. Pironio, A. Acín, N. Brunner, N. Gisin, S. Massar, and V. Scarani, Device-independent quantum key distribution secure against collective attacks, New J. Phys. 11(4), 045021 (2009)

[35] L. Masanes, S. Pironio, and A. Acín, Secure deviceindependent quantum key distribution with causally independent measurement devices, Nat. Commun. 2(1), 238 (2011)

[36] A. Máttar, J. Kolodynski, P. Skrzypczyk, D. Cavalcanti, K. Banaszek, and A. Acín, Device-independent quantum key distribution with single-photon sources, arXiv: 1803.07089 (2018)

[37] H. K. Lo, M. Curty, and B. Qi, Measurementdeviceindependent quantum key distribution, Phys. Rev. Lett. 108(13), 130503 (2012)

[38] Y. Liu, T. Y. Chen, L. J. Wang, H. Liang, G. L. Shentu, J. Wang, K. Cui, H. L. Yin, N. L. Liu, L. Li, X. Ma, J. S. Pelc, M. M. Fejer, C. Z. Peng, Q. Zhang, and J. W. Pan, Experimental measurement-device-independent quantum key distribution, Phys. Rev. Lett. 111(13), 130502 (2013)

[39] F. H. Xu, M. Curty, B. Qi, and H. K. Lo, Practical aspects of measurement-device-independent quantum key distribution, New J. Phys. 15(11), 113007 (2013)

[40] Z. Y. Tang, Z. F. Liao, F. H. Xu, B. Qi, L. Qian, and H. K. Lo, Experimental demonstration of polarization encoding measurement-device-independent quantum key distribution, Phys. Rev. Lett. 112(19), 190503 (2014)

[41] Y. L. Tang, H. L. Yin, S. J. Chen, Y. Liu, W. J. Zhang, X. Jiang, L. Zhang, J. Wang, L. X. You, J. Y. Guan, D. X. Yang, Z. Wang, H. Liang, Z. Zhang, N. Zhou, X. Ma, T. Y. Chen, Q. Zhang, and J. W. Pan, Measurement-deviceindependent quantum key distribution over 200 km, Phys. Rev. Lett. 114(6), 069901 (2015)

[42] H. L. Yin, W. F. Cao, Y. Fu, Y. L. Tang, Y. Liu, T. Y. Chen, and Z. B. Chen, Long-distance measurement-deviceindependent quantum key distribution with coherent-state superpositions, Opt. Lett. 39(18), 5451 (2014)

[43] C. Wang, X. T. Song, Z. Q. Yin, S. Wang, W. Chen, C. M. Zhang, G. C. Guo, and Z. F. Han, Phase-reference-free experiment of measurement-device-independent quantum key distribution, Phys. Rev. Lett. 115(16), 160502 (2015)

[44] H. L. Yin, T. Y. Chen, Z. W. Yu, H. Liu, L. X. You, Y. H. Zhou, S. J. Chen, Y. Mao, M. Q. Huang, W. J. Zhang, H. Chen, M. J. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X. B. Wang, and J. W. Pan, Measurement deviceindependent quantum key distribution over a 404 km optical fiber, Phys. Rev. Lett. 117(19), 190501 (2016)

[45] C. Wang, Z. Q. Yin, S. Wang, W. Chen, G. C. Guo, and Z. F. Han, Measurement-device-independent quantum key distribution robust against environmental disturbances, Optica 4(9), 1016 (2017)

[46] X. D. Wu, Y. J. Wang, D. Huang, and Y. Guo, Simultaneous measurement-device-independent continuous variable quantum key distribution with realistic detector compensation, Front. Phys. 15(3), 31601 (2020)

[47] J. Mower, Z. S. Zhang, P. Desjardins, C. Lee, J. H. Shapiro, and D. Englund, High-dimensional quantum key distribution using dispersive optics, Phys. Rev. A 87(6), 062322 (2013)

[48] M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, Higherdimensional orbitalangular-momentum-based quantum key distribution with mutually unbiased bases, Phys. Rev. A 88(3), 032305 (2013)

[49] T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, R. P. Mirin, T. Gerrits, S. W. Nam, F. Marsili, M. D. Shaw, Z. Zhang, L. Wang, D. Englund, G. W. Wornell, J. H. Shapiro, and F. N. C. Wong, Photon-efficient quantum key distribution using time–energy entanglement with high-dimensional encoding, New J. Phys. 17(2), 022002 (2015)

[50] D. Bunandar, Z. S. Zhang, J. H. Shapiro, and D. R. Englund, Practical high-dimensional quantum key distribution with decoy states, Phys. Rev. A 91(2), 022336 (2015)

[51] S. Wang, Z. Q. Yin, W. Chen, D. Y. He, X. T. Song, H. W. Li, L. J. Zhang, Z. Zhou, G. C. Guo, and Z. F. Han, Experimental demonstration of a quantum key distribution without signal disturbance monitoring, Nat. Photonics 9(12), 832 (2015)

[52] H. Z. Bao, W. S. Bao, Y. Wang, R. K. Chen, and H. W. Li, Detector-decoy high-dimensional quantum key distribution, Opt. Express 24(19), 22159 (2016)

[53] H. Chau, C. Wong, Q. Wang, and T. Huang, Qudit-based measurement-device-independent quantum key distribution using linear optics, arXiv: 1608.08329 (2016)

[54] F. T. Tabesh, S. Salimi, and A. S. Khorashad, Witness for initial correlations among environments, Phys. Rev. A 95(5), 052323 (2017)

[55] G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. F. da Silva, G. B. Xavier, and G. Lima, High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers, Phys. Rev. A 96(2), 022317 (2017)

[56] L. Dellantonio, A. S. Sorensen, and D. Bacco, Highdimensional measurement-device-independent quantum key distribution on two-dimensional subspaces, Phys. Rev. A 98(6), 062301 (2018)

[57] G. I. Struchalin, E. V. Kovlakov, S. S. Straupe, and S. P. Kulik, Adaptive quantum tomography of highdimensional bipartite systems, Phys. Rev. A 98(3), 032330 (2018)

[58] S. Wang, Z. Q. Yin, H. F. Chau, W. Chen, C. Wang, G. C. Guo, and Z. F. Han, Proof-of-principle experimental realization of a qubit-like qudit-based quantum key distribution scheme, Quan. Sci. Technol. 3(2), 025006 (2018)

[59] F. M. Wang, P. Zeng, J. P. Zhao, B. Braverman, Y. Zhou, M. Mirhosseini, X. Wang, H. Gao, F. Li, R. W. Boyd, and P. Zhang, High-dimensional quantum key distribution based on mutually partially unbiased bases, Phys. Rev. A 101(3), 032340 (2020)

[60] F. X. Wang, W. Chen, Z. Q. Yin, S. Wang, G. C. Guo, and Z. F. Han, Characterizing high-quality highdimensional quantum key distribution by state mapping between different degrees of freedom, Phys. Rev. A 11, 024070 (2019)

[61] J. Chapman, C. Lim, and P. Kwiat, Hyperentangled timebin and polarization quantum key distribution, arXiv: 1908.09018 (2019)

[62] Z. X. Cui, W. Zhong, L. Zhou, and Y. B. Sheng, Measurement-device-independent quantum key distribution with hyper-encoding, Sci. China Phys. Mech. Astron. 62(11), 110311 (2019)

[63] X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, Quantum teleportation of multiple degrees of freedom of a single photon, Nature 518(7540), 516 (2015)

[64] X. M. Hu, Y. Guo, B. H. Liu, Y. F. Huang, C. F. Li, and G. C. Guo, Beating the channel capacity limit for superdense coding with entangled ququarts, Sci. Adv. 4(7), eaat9304 (2018)

[65] F. Z. Wu, G. J. Yang, H. B. Wang, J. Xiong, F. Alzahrani, A. Hobiny, and F. G. Deng, High-capacity quantum secure direct communication with two-photon six-qubit hyperentangled states, Sci. China Phys. Mech. Astron. 60(12), 120313 (2017)

[66] S. S. Chen, L.Zhou, W. Zhong, and Y. B. Sheng, Threestep three-party quantum secure direct communication, Sci. China Phys. Mech. Astron. 61(9), 90312 (2018)

[67] L. Y. Li, T. J. Wang, and C. Wang, The analysis of highcapacity quantum secure direct communication using polarization and orbital angular momentum of photons, Mod. Phys. Lett. B 34(02), 2050017 (2020)

[68] G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, Hyper-entanglement of two photons in three degrees of freedom, Phys. Rev. A 79(3), 030301 (2009)

[69] Q. Liu, G. Y. Wang, Q. Ai, M. Zhang, and F. G. Deng, Complete nondestructive analysis of two-photon six-qubit hyperentangled Bell states assisted by cross-Kerr nonlinearity, Sci. Rep. 6(1), 22016 (2016)

[70] H. Inamori, Security of practical time-reversed EPR quantum key distribution, Algorithmica 34(4), 340 (2002)

[71] P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Linear optical quantum computing with photonic qubits, Rev. Mod. Phys. 79(1), 135 (2007)

[72] Y. B. Wei, W. Q. Liu, and N. Y. Chen, Implementing twophoton three-degree-of-freedom hyper-parallel controlled phase flip gate through cavity-assisted interactions, Ann. Phys. 532(4), 1900578 (2020)

[73] C. Zhu and G. Huang, Giant Kerr nonlinearity, controlled entangled photons and polarization phase gates in coupled quantum-well structures, Opt. Express 19(23), 23364 (2011)

[74] I. C. Hoi, A. F. Kockum, T. Palomaki, T. M. Stace, B. Fan, L. Tornberg, S. R. Sathyamoorthy, G. Johansson, P. Delsing, and C. M. Wilson, Giant cross-Kerr effect for propagating microwaves induced by an artificial atom, Phys. Rev. Lett. 111(5), 053601 (2013)

[75] K. M. Beck, M. Hosseini, Y. H. Duan, and V. Vuletic, Large conditional single-photon cross-phase modulation,Proc. Natl. Acad. Sci. USA 113(35), 9740 (2016)

[76] D. Tiarks, S. Schmidt, G. Rempe, and S. Dürr, Optical π phase shift created with a single-photon pulse, Sci. Adv. 2(4), e1600036 (2016)

[77] J. Sinclair, D. Angulo, N. Lupu-Gladstein, K. Bonsma-Fisher, and A. M. Steinberg, Observation of a large, resonant, cross-Kerr nonlinearity in a free-space Rydberg medium, arXiv: 1906.05151 (2019)

[78] B. C. Ren, H. R. Wei, M. Hua, T. Li, and F. G. Deng, Complete hyperentangled-Bell-state analysis for photon systems assisted by quantum-dot spins in optical microcavities, Opt. Express 20(22), 24664 (2012)

[79] T. J. Wang, Y. Lu, and G. L. Long, Generation and complete analysis of the hyperentangled Bell state for photons assisted by quantum-dot spins in optical microcavities, Phys. Rev. A 86(4), 042337 (2012)

[80] G. Y. Wang, Q. Ai, B. C. Ren, T. Li, and F. G. Deng, Error-detected generation and complete analysis of hyperentangled Bell states for photons assisted by quantum-dot spins in double-sided optical microcavities, Opt. Express 24(25), 28444 (2016)

[81] Q. Liu and M. Zhang, Generation and complete nondestructive analysis of hyperentanglement assisted by nitrogen-vacancy centers in resonators, Phys. Rev. A 91(6), 062321 (2015)

[82] T. J. Wang and C. Wang, Complete hyperentangled-Bell state analysis for photonic qubits assisted by a three-level Λ-type system, Sci. Rep. 6(1), 19497 (2016)

RIGHTS & PERMISSIONS

2021 Higher Education Press