Abstract

Remote distribution of secret keys is a challenging task in quantum cryptography. A significant step in this direction is the measurement-device independence quantum key distribution (MDI-QKD). For two remote (or independent) parties Alice and Bob who initially no share secret information, the MDI-QKD enables them to share a secret key by the measurement of an untrusted relay. Unfortunately, the MDI-QKD yields the assumption that the devices of both Alice and Bob have to be trusted. Here, we show that QKD between two independent parties can also be realized even if the device of either Alice or Bob is untrusted. We tackle the problem by resorting to the recently developed one-sided device-independent QKD protocol. We derive conditions on the extracted secret key to be unconditionally secure against arbitary attacks in the limit of asymptotic keys. In the presence of Gaussian states and measurements, we theoretically demonstrate our scheme is feasible, which could be an attractive candidate for long distance secret communication.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (1)

Y. Xiang, X. Su, L. Mišta, G. Adesso, and Q. He, “Multipartite einstein-podolsky-rosen steering sharing with separable states,” Phys. Rev. A 99(1), 010104 (2019).
[Crossref]

2018 (1)

N. Wang, S. Du, W. Liu, X. Wang, Y. Li, and K. Peng, “Long-distance continuous-variable quantum key distribution with entangled states,” Phys. Rev. Appl. 10(6), 064028 (2018).
[Crossref]

2017 (4)

H.-Z. Bao, W.-S. Bao, Y. Wang, R.-K. Chen, H.-X. Ma, C. Zhou, and H.-W. Li, “Time-energy high-dimensional one-side device-independent quantum key distribution,” Chin. Phys. B 26(5), 050302 (2017).
[Crossref]

Y. Xiang, I. Kogias, G. Adesso, and Q. He, “Multipartite gaussian steering: Monogamy constraints and quantum cryptography applications,” Phys. Rev. A 95(1), 010101 (2017).
[Crossref]

Y.-M. Li, X.-Y. Wang, Z.-L. Bai, W.-Y. Liu, S.-S. Yang, and K.-C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B 26(4), 040303 (2017).
[Crossref]

W. Rosenfeld, D. Burchardt, R. Garthoff, K. Redeker, N. Ortegel, M. Rau, and H. Weinfurter, “Event-ready bell test using entangled atoms simultaneously closing detection and locality loopholes,” Phys. Rev. Lett. 119(1), 010402 (2017).
[Crossref]

2016 (6)

E. Diamanti, H.-K. Lo, B. Qi, and Z. Yuan, “Practical challenges in quantum key distribution,” npj Quantum Inf. 2(1), 16025 (2016).
[Crossref]

X. Su, C. Tian, X. Deng, Q. Li, C. Xie, and K. Peng, “Quantum entanglement swapping between two multipartite entangled states,” Phys. Rev. Lett. 117(24), 240503 (2016).
[Crossref]

N. Walk, S. Hosseini, J. Geng, O. Thearle, J. Y. Haw, S. Armstrong, S. M. Assad, J. Janousek, T. C. Ralph, T. Symul, H. M. Wiseman, and P. K. Lam, “Experimental demonstration of gaussian protocols for one-sided device-independent quantum key distribution,” Optica 3(6), 634 (2016).
[Crossref]

L. C. Comandar, M. Lucamarini, B. Fröhlich, J. F. Dynes, A. W. Sharpe, S. W.-B. Tam, Z. L. Yuan, R. V. Penty, and A. J. Shields, “Quantum key distribution without detector vulnerabilities using optically seeded lasers,” Nat. Photonics 10(5), 312–315 (2016).
[Crossref]

Y.-H. Zhou, Z.-W. Yu, and X.-B. Wang, “Making the decoy-state measurement-device-independent quantum key distribution practically useful,” Phys. Rev. A 93(4), 042324 (2016).
[Crossref]

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-device-independent quantum key distribution over a 404 km optical fiber,” Phys. Rev. Lett. 117(19), 190501 (2016).
[Crossref]

2015 (4)

S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9(6), 397–402 (2015).
[Crossref]

Y. Fu, H.-L. Yin, T.-Y. Chen, and Z.-B. Chen, “Long-distance measurement-device-independent multiparty quantum communication,” Phys. Rev. Lett. 114(9), 090501 (2015).
[Crossref]

T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, “Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks,” Nat. Commun. 6(1), 8795 (2015).
[Crossref]

B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526(7575), 682–686 (2015).
[Crossref]

2014 (6)

F. Furrer, M. Berta, M. Tomamichel, V. B. Scholz, and M. Christandl, “Position-momentum uncertainty relations in the presence of quantum memory,” J. Math. Phys. 55(12), 122205 (2014).
[Crossref]

V. C. Usenko, L. Ruppert, and R. Filip, “Entanglement-based continuous-variable quantum key distribution with multimode states and detectors,” Phys. Rev. A 90(6), 062326 (2014).
[Crossref]

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-device-independent quantum key distribution over 200 km,” Phys. Rev. Lett. 113(19), 190501 (2014).
[Crossref]

Z. Li, Y.-C. Zhang, F. Xu, X. Peng, and H. Guo, “Continuous-variable measurement-device-independent quantum key distribution,” Phys. Rev. A 89(5), 052301 (2014).
[Crossref]

Y.-C. Zhang, Z. Li, S. Yu, W. Gu, X. Peng, and H. Guo, “Continuous-variable measurement-device-independent quantum key distribution using squeezed states,” Phys. Rev. A 90(5), 052325 (2014).
[Crossref]

H.-K. Lo, M. Curty, and K. Tamaki, “Secure quantum key distribution,” Nat. Photonics 8(8), 595–604 (2014).
[Crossref]

2013 (5)

M. Tomamichel, S. Fehr, J. Kaniewski, and S. Wehner, “A monogamy-of-entanglement game with applications to device-independent quantum cryptography,” New J. Phys. 15(10), 103002 (2013).
[Crossref]

Y. Wang, W.-s. Bao, H.-w. Li, C. Zhou, and Y. Li, “Finite-key analysis for one-sided device-independent quantum key distribution,” Phys. Rev. A 88(5), 052322 (2013).
[Crossref]

R. L. Frank and E. H. Lieb, “Extended quantum conditional entropy and quantum uncertainty inequalities,” Commun. Math. Phys. 323(2), 487–495 (2013).
[Crossref]

B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat, “Detection-loophole-free test of quantum nonlocality, and applications,” Phys. Rev. Lett. 111(13), 130406 (2013).
[Crossref]

M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. Kofler, J. Beyer, A. Lita, B. Calkins, T. Gerrits, S. W. Nam, R. Ursin, and A. Zeilinger, “Bell violation using entangled photons without the fair-sampling assumption,” Nature 497(7448), 227–230 (2013).
[Crossref]

2012 (5)

M. Tomamichel, C. C. W. Lim, N. Gisin, and R. Renner, “Tight finite-key analysis for quantum cryptography,” Nat. Commun. 3(1), 634 (2012).
[Crossref]

C. Branciard, E. G. Cavalcanti, S. P. Walborn, V. Scarani, and H. M. Wiseman, “One-sided device-independent quantum key distribution: Security, feasibility, and the connection with steering,” Phys. Rev. A 85(1), 010301 (2012).
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C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).
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S. L. Braunstein and S. Pirandola, “Side-channel-free quantum key distribution,” Phys. Rev. Lett. 108(13), 130502 (2012).
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H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108(13), 130503 (2012).
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2011 (3)

M. Tomamichel and R. Renner, “Uncertainty relation for smooth entropies,” Phys. Rev. Lett. 106(11), 110506 (2011).
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I. Gerhardt, Q. Liu, A. Lamas-Linares, J. Skaar, C. Kurtsiefer, and V. Makarov, “Full-field implementation of a perfect eavesdropper on a quantum cryptography system,” Nat. Commun. 2(1), 349 (2011).
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C. Wiechers, L. Lydersen, C. Wittmann, D. Elser, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “After-gate attack on a quantum cryptosystem,” New J. Phys. 13(1), 013043 (2011).
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2010 (3)

F. Xu, B. Qi, and H.-K. Lo, “Experimental demonstration of phase-remapping attack in a practical quantum key distribution system,” New J. Phys. 12(11), 113026 (2010).
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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), 686–689 (2010).
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M. Berta, M. Christandl, R. Colbeck, J. M. Renes, and R. Renner, “The uncertainty principle in the presence of quantum memory,” Nat. Phys. 6(9), 659–662 (2010).
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2009 (4)

J. M. Renes and J.-C. Boileau, “Conjectured strong complementary information tradeoff,” Phys. Rev. Lett. 103(2), 020402 (2009).
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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).
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S. Nauerth, M. Fürst, T. Schmitt-Manderbach, H. Weier, and H. Weinfurter, “Information leakage via side channels in freespace bb84 quantum cryptography,” New J. Phys. 11(6), 065001 (2009).
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V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
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2008 (2)

R. Renner, “Security of quantum key distribution,” Int. J. Quant. Inf. 06(01), 1–127 (2008).
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Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, and H.-K. Lo, “Quantum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems,” Phys. Rev. A 78(4), 042333 (2008).
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2007 (2)

A. Lamas-Linares and C. Kurtsiefer, “Breaking a quantum key distribution system through a timing side channel,” Opt. Express 15(15), 9388–9393 (2007).
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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).
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2006 (2)

V. Makarov, A. Anisimov, and J. Skaar, “Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 74(2), 022313 (2006).
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C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Coherent-state quantum key distribution without random basis switching,” Phys. Rev. A 73(2), 022316 (2006).
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2005 (3)

A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. 95(18), 180503 (2005).
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I. Devetak and A. Winter, “Distillation of secret key and entanglement from quantum states,” Proc. R. Soc. A 461(2053), 207–235 (2005).
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R. Renner, N. Gisin, and B. Kraus, “Information-theoretic security proof for quantum-key-distribution protocols,” Phys. Rev. A 72(1), 012332 (2005).
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2004 (5)

I. Devetak and A. Winter, “Relating quantum privacy and quantum coherence: An operational approach,” Phys. Rev. Lett. 93(8), 080501 (2004).
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X. Jia, X. Su, Q. Pan, J. Gao, C. Xie, and K. Peng, “Experimental demonstration of unconditional entanglement swapping for continuous variables,” Phys. Rev. Lett. 93(25), 250503 (2004).
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S. Iblisdir, G. Van Assche, and N. J. Cerf, “Security of quantum key distribution with coherent states and homodyne detection,” Phys. Rev. Lett. 93(17), 170502 (2004).
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C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
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H. Yonezawa, T. Aoki, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variables,” Nature 431(7007), 430–433 (2004).
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2003 (2)

F. Grosshans, G. V. Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature 421(6920), 238–241 (2003).
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F. Grosshans, N. J. Cerf, P. Grangier, J. Wenger, and R. Tualle-Brouri, “Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables,” Quant. Inf. Comp. 3, 535–552 (2003).

2002 (2)

F. Grosshans and P. Grangier, “Continuous variable quantum cryptography using coherent states,” Phys. Rev. Lett. 88(5), 057902 (2002).
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N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
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2001 (3)

N. J. Cerf, M. Lévy, and G. V. Assche, “Quantum distribution of gaussian keys using squeezed states,” Phys. Rev. A 63(5), 052311 (2001).
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D. Gottesman and J. Preskill, “Secure quantum key distribution using squeezed states,” Phys. Rev. A 63(2), 022309 (2001).
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S. Félix, N. Gisin, A. Stefanov, and H. Zbinden, “Faint laser quantum key distribution: Eavesdropping exploiting multiphoton pulses,” J. Mod. Opt. 48(13), 2009–2021 (2001).
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2000 (3)

M. Hillery, “Quantum cryptography with squeezed states,” Phys. Rev. A 61(2), 022309 (2000).
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T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84(20), 4729–4732 (2000).
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A. Cabello, “Quantum key distribution without alternative measurements,” Phys. Rev. A 61(5), 052312 (2000).
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1999 (2)

T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61(1), 010303 (1999).
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R. E. S. Polkinghorne and T. C. Ralph, “Continuous variable entanglement swapping,” Phys. Rev. Lett. 83(11), 2095–2099 (1999).
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1998 (2)

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282(5389), 706–709 (1998).
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S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80(4), 869–872 (1998).
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1993 (1)

M. Żukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, “"event-ready-detectors"bell experiment via entanglement swapping,” Phys. Rev. Lett. 71(26), 4287–4290 (1993).
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1992 (1)

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without bell’s theorem,” Phys. Rev. Lett. 68(5), 557–559 (1992).
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1991 (1)

A. K. Ekert, “Quantum cryptography based on bell’s theorem,” Phys. Rev. Lett. 67(6), 661–663 (1991).
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1973 (1)

A. S. Holevo, “Some estimates for the amount of information transmittable by a quantum communications channel,” Probl. Peredachi Inf. 9, 3 (1973).

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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).
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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).
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Y. Xiang, X. Su, L. Mišta, G. Adesso, and Q. He, “Multipartite einstein-podolsky-rosen steering sharing with separable states,” Phys. Rev. A 99(1), 010104 (2019).
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Y. Xiang, I. Kogias, G. Adesso, and Q. He, “Multipartite gaussian steering: Monogamy constraints and quantum cryptography applications,” Phys. Rev. A 95(1), 010101 (2017).
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B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat, “Detection-loophole-free test of quantum nonlocality, and applications,” Phys. Rev. Lett. 111(13), 130406 (2013).
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S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9(6), 397–402 (2015).
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V. Makarov, A. Anisimov, and J. Skaar, “Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 74(2), 022313 (2006).
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H. Yonezawa, T. Aoki, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variables,” Nature 431(7007), 430–433 (2004).
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Assad, S. M.

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F. Grosshans, G. V. Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature 421(6920), 238–241 (2003).
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N. J. Cerf, M. Lévy, and G. V. Assche, “Quantum distribution of gaussian keys using squeezed states,” Phys. Rev. A 63(5), 052311 (2001).
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Y.-M. Li, X.-Y. Wang, Z.-L. Bai, W.-Y. Liu, S.-S. Yang, and K.-C. Peng, “Continuous variable quantum key distribution,” Chin. Phys. B 26(4), 040303 (2017).
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H.-Z. Bao, W.-S. Bao, Y. Wang, R.-K. Chen, H.-X. Ma, C. Zhou, and H.-W. Li, “Time-energy high-dimensional one-side device-independent quantum key distribution,” Chin. Phys. B 26(5), 050302 (2017).
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H.-Z. Bao, W.-S. Bao, Y. Wang, R.-K. Chen, H.-X. Ma, C. Zhou, and H.-W. Li, “Time-energy high-dimensional one-side device-independent quantum key distribution,” Chin. Phys. B 26(5), 050302 (2017).
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C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without bell’s theorem,” Phys. Rev. Lett. 68(5), 557–559 (1992).
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C. H. Bennett and G. Brassard, “Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India,” (IEEE, New York, 1984), p. 175.

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F. Furrer, M. Berta, M. Tomamichel, V. B. Scholz, and M. Christandl, “Position-momentum uncertainty relations in the presence of quantum memory,” J. Math. Phys. 55(12), 122205 (2014).
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M. Berta, M. Christandl, R. Colbeck, J. M. Renes, and R. Renner, “The uncertainty principle in the presence of quantum memory,” Nat. Phys. 6(9), 659–662 (2010).
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Beyer, J.

M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. Kofler, J. Beyer, A. Lita, B. Calkins, T. Gerrits, S. W. Nam, R. Ursin, and A. Zeilinger, “Bell violation using entangled photons without the fair-sampling assumption,” Nature 497(7448), 227–230 (2013).
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B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526(7575), 682–686 (2015).
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J. M. Renes and J.-C. Boileau, “Conjectured strong complementary information tradeoff,” Phys. Rev. Lett. 103(2), 020402 (2009).
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C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Coherent-state quantum key distribution without random basis switching,” Phys. Rev. A 73(2), 022316 (2006).
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C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
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C. Branciard, E. G. Cavalcanti, S. P. Walborn, V. Scarani, and H. M. Wiseman, “One-sided device-independent quantum key distribution: Security, feasibility, and the connection with steering,” Phys. Rev. A 85(1), 010301 (2012).
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C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without bell’s theorem,” Phys. Rev. Lett. 68(5), 557–559 (1992).
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C. H. Bennett and G. Brassard, “Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India,” (IEEE, New York, 1984), p. 175.

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S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S. L. Braunstein, S. Lloyd, T. Gehring, C. S. Jacobsen, and U. L. Andersen, “High-rate measurement-device-independent quantum cryptography,” Nat. Photonics 9(6), 397–402 (2015).
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[Crossref]

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S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80(4), 869–872 (1998).
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F. Grosshans, G. V. Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature 421(6920), 238–241 (2003).
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B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat, “Detection-loophole-free test of quantum nonlocality, and applications,” Phys. Rev. Lett. 111(13), 130406 (2013).
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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).
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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).
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B. G. Christensen, K. T. McCusker, J. B. Altepeter, B. Calkins, T. Gerrits, A. E. Lita, A. Miller, L. K. Shalm, Y. Zhang, S. W. Nam, N. Brunner, C. C. W. Lim, N. Gisin, and P. G. Kwiat, “Detection-loophole-free test of quantum nonlocality, and applications,” Phys. Rev. Lett. 111(13), 130406 (2013).
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C. Branciard, E. G. Cavalcanti, S. P. Walborn, V. Scarani, and H. M. Wiseman, “One-sided device-independent quantum key distribution: Security, feasibility, and the connection with steering,” Phys. Rev. A 85(1), 010301 (2012).
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Cerf, N. J.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).
[Crossref]

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
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[Crossref]

F. Grosshans, G. V. Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature 421(6920), 238–241 (2003).
[Crossref]

F. Grosshans, N. J. Cerf, P. Grangier, J. Wenger, and R. Tualle-Brouri, “Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables,” Quant. Inf. Comp. 3, 535–552 (2003).

N. J. Cerf, M. Lévy, and G. V. Assche, “Quantum distribution of gaussian keys using squeezed states,” Phys. Rev. A 63(5), 052311 (2001).
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Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, and H.-K. Lo, “Quantum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems,” Phys. Rev. A 78(4), 042333 (2008).
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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-device-independent quantum key distribution over a 404 km optical fiber,” Phys. Rev. Lett. 117(19), 190501 (2016).
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H.-Z. Bao, W.-S. Bao, Y. Wang, R.-K. Chen, H.-X. Ma, C. Zhou, and H.-W. Li, “Time-energy high-dimensional one-side device-independent quantum key distribution,” Chin. Phys. B 26(5), 050302 (2017).
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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-device-independent quantum key distribution over a 404 km optical fiber,” Phys. Rev. Lett. 117(19), 190501 (2016).
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Chen, Z.-B.

Y. Fu, H.-L. Yin, T.-Y. Chen, and Z.-B. Chen, “Long-distance measurement-device-independent multiparty quantum communication,” Phys. Rev. Lett. 114(9), 090501 (2015).
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Christandl, M.

F. Furrer, M. Berta, M. Tomamichel, V. B. Scholz, and M. Christandl, “Position-momentum uncertainty relations in the presence of quantum memory,” J. Math. Phys. 55(12), 122205 (2014).
[Crossref]

M. Berta, M. Christandl, R. Colbeck, J. M. Renes, and R. Renner, “The uncertainty principle in the presence of quantum memory,” Nat. Phys. 6(9), 659–662 (2010).
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Figures (6)

Fig. 1.
Fig. 1. Diagrammatic sketch of EB QKDTP scheme. The table summaries the QKD protocols for different cases of QKDTP scheme. The tick and cross symbols denote trusted and untrusted, respectively.
Fig. 2.
Fig. 2. EB scheme of QKDTP based on 1sDI security.
Fig. 3.
Fig. 3. Secret key rate $K$ versus transmission distance $L$ in the EB QKDTP based on 1sDI security.
Fig. 4.
Fig. 4. Secret key rate $K$ versus transmission distances $L_{A}$ and $L_{B}$ in the EB QKDTP based on 1sDI security.
Fig. 5.
Fig. 5. Hybrid scheme of QKDTP based on 1sDI security.
Fig. 6.
Fig. 6. Secret key rate $K$ versus transmission distance in the hybrid scheme of 1sDI QKDTP. (a), symmetric case. (b), asymmetric case.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

A ^ 1 = cosh ( r ) a ^ 1 + sinh ( r ) a ^ 2 ,   A ^ 2 = cosh ( r ) a ^ 2 + sinh ( r ) a ^ 1 , B ^ 1 = cosh ( r ) b ^ 1 + sinh ( r ) b ^ 2 ,   B ^ 2 = cosh ( r ) b ^ 2 + sinh ( r ) b ^ 1 ,
A ^ 2 = η A A ^ 2 + 1 η A ν ^ A ,   B ^ 2 = η B B ^ 2 + 1 η B ν ^ B ,
A ^ 1 = A ^ 1 + ξ i ^ 1 + i ξ i ^ 2 ,
K β I ( X A 1 : X B 1 ) χ ( X A 1 : E ) .
I ( X A 1 : X B 1 ) = H ( X A 1 ) H ( X A 1 | X B 1 ) .
I ( X A 1 : X B 1 ) = log 2 V ( X A 1 ) V ( X A 1 | X B 1 ) .
χ ( X A 1 : E ) S ( ρ E ) d X A 1 p ( X A 1 ) S ( ρ E | X A 1 ) ,
S ( X A 1 | E ) = H ( X A 1 ) + d X A 1 p ( X A 1 ) S ( ρ E | X A 1 ) S ( ρ E ) .
χ ( X A 1 | E ) H ( X A 1 ) S ( X A 1 | E ) .
S ( X A 1 | E ) + S ( Y A 1 | B ) log 2 2 π ,
χ ( X A 1 | E ) H ( X A 1 ) + S ( Y A 1 | B ) log 2 2 π .
χ ( X A 1 | E ) log 2 2 π e V ( X A 1 ) V ( Y A 1 | Y B ) log 2 2 π .
K β log 2 V ( X A 1 ) V ( X A 1 | X B 1 ) + log 2 2 e V ( X A 1 ) V ( Y A 1 | Y B 1 ) .
K β log 2 V ( X A ) V ( X A | X B 1 ) + log 2 2 e V ( X A ) V ( Y A | Y B 1 ) .

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