Proof-of-principle demonstration of measurement-device-independent quantum key distribution based on intrinsically stable polarization-modulated units

Yi-ping Yuan; Cong Du; Qi-qi Shen; Jin-dong Wang; Ya-fei Yu; Zheng-jun Wei; Zhao-xi Chen; Zhi-ming Zhang

doi:10.1364/OE.387968

Optics Express
Vol. 28,
Issue 8,
pp. 10772-10782
(2020)
•https://doi.org/10.1364/OE.387968

Proof-of-principle demonstration of measurement-device-independent quantum key distribution based on intrinsically stable polarization-modulated units

Yi-ping Yuan, Cong Du, Qi-qi Shen, Jin-dong Wang, Ya-fei Yu, Zheng-jun Wei, Zhao-xi Chen, and Zhi-ming Zhang

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Yi-ping Yuan, Cong Du, Qi-qi Shen, Jin-dong Wang, Ya-fei Yu, Zheng-jun Wei, Zhao-xi Chen, and Zhi-ming Zhang, "Proof-of-principle demonstration of measurement-device-independent quantum key distribution based on intrinsically stable polarization-modulated units," Opt. Express 28, 10772-10782 (2020)

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Abstract

The experimental demonstration of measurement-device-independent quantum key distribution (MDI-QKD) has been widely demonstrated. Thus far, several experimental groups have implemented polarization encoding MDI-QKD but with manual polarization controllers, or polarization modulators that make circular polarization states unstable. Here, we apply an intrinsically stable polarization-modulated unit (PMU) to MDI-QKD so that Alice and Bob can modulate four BB84 polarization states, all of which can be kept stable from even the harsh environment. Moreover, our PMU can provide two operational polarization encoding modes suitable to different application scenarios. A proof-of-principle demonstration of MDI-QKD based on our PMU is implemented with an interference visibility of 46.6%, an average quantum bit error rate of 1.49% for the Z basis and the secure key rate of 4.25 × 10⁻⁶ bits per pulse. The proposed study is helpful for building polarization encoding MDI-QKD systems with better stability.

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References

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Year
Author
Publication

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]
A. K. Ekert, “Quantum cryptography based on bell’s theorem,” Phys. Rev. Lett. 67(6), 661–663 (1991).
[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).
[Crossref]
D. Mayers, “Unconditional security in quantum cryptography,” J. Assoc. Comput. Mach. 48(3), 351–406 (2001).
[Crossref]
H.-K. Lo and H. F. Chau, “Unconditional security of quantum key distribution over arbitrarily long distances,” Science 283(5410), 2050–2056 (1999).
[Crossref]
Z. L. Yuan, J. F. Dynes, and A. J. Shields, “Resilience of gated avalanche photodiodes against bright illumination attacks in quantum cryptography,” Appl. Phys. Lett. 98(23), 231104 (2011).
[Crossref]
C.-H. F. Fung, B. Qi, K. Tamaki, and H.-K. Lo, “Phase-remapping attack in practical quantum-key-distribution systems,” Phys. Rev. A 75(3), 032314 (2007).
[Crossref]
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).
[Crossref]
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).
[Crossref]
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).
[Crossref]
H. Weier, H. Krauss, M. Rau, M. Fürst, S. Nauerth, and H. Weinfurter, “Quantum eavesdropping without interception: an attack exploiting the dead time of single-photon detectors,” New J. Phys. 13(7), 073024 (2011).
[Crossref]
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).
[Crossref]
A. Acín, N. Gisin, and L. Masanes, “From bell’s theorem to secure quantum key distribution,” Phys. Rev. Lett. 97(12), 120405 (2006).
[Crossref]
V. Makarov, A. Anisimov, and J. Skaar, “Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 74(2), 022313 (2006).
[Crossref]
V. Makarov and D. R. Hjelme, “Faked states attack on quantum cryptosystems,” J. Mod. Opt. 52(5), 691–705 (2005).
[Crossref]
H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108(13), 130503 (2012).
[Crossref]
Q. Zhang, F. Xu, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Large scale quantum key distribution: challenges and solutions [invited],” Opt. Express 26(18), 24260–24273 (2018).
[Crossref]
R. Valivarthi, Q. Zhou, C. John, F. Marsili, V. B. Verma, M. D. Shaw, S. W. Nam, D. Oblak, and W. Tittel, “A cost-effective measurement-device-independent quantum key distribution system for quantum networks,” Quantum Sci. Technol. 2(4), 04LT01 (2017).
[Crossref]
T. Ferreira da Silva, D. Vitoreti, G. B. Xavier, G. C. do Amaral, G. P. Temporão, and J. P. von der Weid, “Proof-of-principle demonstration of measurement-device-independent quantum key distribution using polarization qubits,” Phys. Rev. A 88(5), 052303 (2013).
[Crossref]
Z. Tang, Z. Liao, F. 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).
[Crossref]
L. Comandar, M. Lucamarini, B. Fröhlich, J. Dynes, A. Sharpe, S.-B. Tam, Z. Yuan, R. Penty, and A. Shields, “Quantum key distribution without detector vulnerabilities using optically seeded lasers,” Nat. Photonics 10(5), 312–315 (2016).
[Crossref]
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).
[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]
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]
I. Lucio-Martinez, P. Chan, X. Mo, S. Hosier, and W. Tittel, “Proof-of-concept of real-world quantum key distribution with quantum frames,” New J. Phys. 11(9), 095001 (2009).
[Crossref]
J. Wang, X. Qin, Y. Jiang, X. Wang, L. Chen, F. Zhao, Z. Wei, and Z. Zhang, “Experimental demonstration of polarization encoding quantum key distribution system based on intrinsically stable polarization-modulated units,” Opt. Express 24(8), 8302–8309 (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]
Y. Zhao, B. Qi, and H.-K. Lo, “Experimental quantum key distribution with active phase randomization,” Appl. Phys. Lett. 90(4), 044106 (2007).
[Crossref]
N. Lütkenhaus, “Security against individual attacks for realistic quantum key distribution,” Phys. Rev. A 61(5), 052304 (2000).
[Crossref]

2018 (1)

Q. Zhang, F. Xu, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Large scale quantum key distribution: challenges and solutions [invited],” Opt. Express 26(18), 24260–24273 (2018).
[Crossref]

2017 (1)

R. Valivarthi, Q. Zhou, C. John, F. Marsili, V. B. Verma, M. D. Shaw, S. W. Nam, D. Oblak, and W. Tittel, “A cost-effective measurement-device-independent quantum key distribution system for quantum networks,” Quantum Sci. Technol. 2(4), 04LT01 (2017).
[Crossref]

2016 (4)

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

J. Wang, X. Qin, Y. Jiang, X. Wang, L. Chen, F. Zhao, Z. Wei, and Z. Zhang, “Experimental demonstration of polarization encoding quantum key distribution system based on intrinsically stable polarization-modulated units,” Opt. Express 24(8), 8302–8309 (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]

2014 (2)

Z. Tang, Z. Liao, F. 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).
[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]

2013 (2)

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).
[Crossref]

T. Ferreira da Silva, D. Vitoreti, G. B. Xavier, G. C. do Amaral, G. P. Temporão, and J. P. von der Weid, “Proof-of-principle demonstration of measurement-device-independent quantum key distribution using polarization qubits,” Phys. Rev. A 88(5), 052303 (2013).
[Crossref]

2012 (1)

H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108(13), 130503 (2012).
[Crossref]

2011 (3)

H. Weier, H. Krauss, M. Rau, M. Fürst, S. Nauerth, and H. Weinfurter, “Quantum eavesdropping without interception: an attack exploiting the dead time of single-photon detectors,” New J. Phys. 13(7), 073024 (2011).
[Crossref]

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).
[Crossref]

Z. L. Yuan, J. F. Dynes, and A. J. Shields, “Resilience of gated avalanche photodiodes against bright illumination attacks in quantum cryptography,” Appl. Phys. Lett. 98(23), 231104 (2011).
[Crossref]

2010 (2)

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).
[Crossref]

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).
[Crossref]

2009 (2)

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).
[Crossref]

I. Lucio-Martinez, P. Chan, X. Mo, S. Hosier, and W. Tittel, “Proof-of-concept of real-world quantum key distribution with quantum frames,” New J. Phys. 11(9), 095001 (2009).
[Crossref]

2008 (1)

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).
[Crossref]

2007 (2)

C.-H. F. Fung, B. Qi, K. Tamaki, and H.-K. Lo, “Phase-remapping attack in practical quantum-key-distribution systems,” Phys. Rev. A 75(3), 032314 (2007).
[Crossref]

Y. Zhao, B. Qi, and H.-K. Lo, “Experimental quantum key distribution with active phase randomization,” Appl. Phys. Lett. 90(4), 044106 (2007).
[Crossref]

2006 (2)

A. Acín, N. Gisin, and L. Masanes, “From bell’s theorem to secure quantum key distribution,” Phys. Rev. Lett. 97(12), 120405 (2006).
[Crossref]

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

2005 (1)

V. Makarov and D. R. Hjelme, “Faked states attack on quantum cryptosystems,” J. Mod. Opt. 52(5), 691–705 (2005).
[Crossref]

2002 (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

2001 (1)

D. Mayers, “Unconditional security in quantum cryptography,” J. Assoc. Comput. Mach. 48(3), 351–406 (2001).
[Crossref]

2000 (1)

N. Lütkenhaus, “Security against individual attacks for realistic quantum key distribution,” Phys. Rev. A 61(5), 052304 (2000).
[Crossref]

1999 (1)

H.-K. Lo and H. F. Chau, “Unconditional security of quantum key distribution over arbitrarily long distances,” Science 283(5410), 2050–2056 (1999).
[Crossref]

1991 (1)

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

Acín, A.

A. Acín, N. Gisin, and L. Masanes, “From bell’s theorem to secure quantum key distribution,” Phys. Rev. Lett. 97(12), 120405 (2006).
[Crossref]

Anisimov, A.

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

Bechmann-Pasquinucci, H.

Cerf, N. J.

Chan, P.

I. Lucio-Martinez, P. Chan, X. Mo, S. Hosier, and W. Tittel, “Proof-of-concept of real-world quantum key distribution with quantum frames,” New J. Phys. 11(9), 095001 (2009).
[Crossref]

Chau, H. F.

H.-K. Lo and H. F. Chau, “Unconditional security of quantum key distribution over arbitrarily long distances,” Science 283(5410), 2050–2056 (1999).
[Crossref]

Chen, C.

Chen, H.

Chen, L.

Chen, S.-J.

Chen, T.-Y.

Chen, Y.-A.

Q. Zhang, F. Xu, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Large scale quantum key distribution: challenges and solutions [invited],” Opt. Express 26(18), 24260–24273 (2018).
[Crossref]

Comandar, L.

Cui, K.

Curty, M.

H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108(13), 130503 (2012).
[Crossref]

do Amaral, G. C.

Dušek, M.

Dynes, J.

Dynes, J. F.

Ekert, A. K.

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

Elser, D.

Fejer, M. M.

Ferreira da Silva, T.

Fröhlich, B.

Fung, C.-H. F.

C.-H. F. Fung, B. Qi, K. Tamaki, and H.-K. Lo, “Phase-remapping attack in practical quantum-key-distribution systems,” Phys. Rev. A 75(3), 032314 (2007).
[Crossref]

Fürst, M.

Gisin, N.

A. Acín, N. Gisin, and L. Masanes, “From bell’s theorem to secure quantum key distribution,” Phys. Rev. Lett. 97(12), 120405 (2006).
[Crossref]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

Guan, J.-Y.

Hjelme, D. R.

V. Makarov and D. R. Hjelme, “Faked states attack on quantum cryptosystems,” J. Mod. Opt. 52(5), 691–705 (2005).
[Crossref]

Hosier, S.

I. Lucio-Martinez, P. Chan, X. Mo, S. Hosier, and W. Tittel, “Proof-of-concept of real-world quantum key distribution with quantum frames,” New J. Phys. 11(9), 095001 (2009).
[Crossref]

Huang, M.-Q.

Jain, N.

Jiang, X.

Jiang, Y.

John, C.

Krauss, H.

Leuchs, G.

Li, L.

Li, M. J.

Liang, H.

Liao, Z.

Liu, H.

Liu, N.-L.

Liu, Y.

Lo, H.-K.

H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108(13), 130503 (2012).
[Crossref]

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).
[Crossref]

C.-H. F. Fung, B. Qi, K. Tamaki, and H.-K. Lo, “Phase-remapping attack in practical quantum-key-distribution systems,” Phys. Rev. A 75(3), 032314 (2007).
[Crossref]

Y. Zhao, B. Qi, and H.-K. Lo, “Experimental quantum key distribution with active phase randomization,” Appl. Phys. Lett. 90(4), 044106 (2007).
[Crossref]

H.-K. Lo and H. F. Chau, “Unconditional security of quantum key distribution over arbitrarily long distances,” Science 283(5410), 2050–2056 (1999).
[Crossref]

Lucamarini, M.

Lucio-Martinez, I.

I. Lucio-Martinez, P. Chan, X. Mo, S. Hosier, and W. Tittel, “Proof-of-concept of real-world quantum key distribution with quantum frames,” New J. Phys. 11(9), 095001 (2009).
[Crossref]

Lütkenhaus, N.

N. Lütkenhaus, “Security against individual attacks for realistic quantum key distribution,” Phys. Rev. A 61(5), 052304 (2000).
[Crossref]

Lydersen, L.

Ma, X.

Makarov, V.

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

V. Makarov and D. R. Hjelme, “Faked states attack on quantum cryptosystems,” J. Mod. Opt. 52(5), 691–705 (2005).
[Crossref]

Mao, Y.

Marquardt, C.

Marsili, F.

Masanes, L.

A. Acín, N. Gisin, and L. Masanes, “From bell’s theorem to secure quantum key distribution,” Phys. Rev. Lett. 97(12), 120405 (2006).
[Crossref]

Mayers, D.

D. Mayers, “Unconditional security in quantum cryptography,” J. Assoc. Comput. Mach. 48(3), 351–406 (2001).
[Crossref]

Mo, X.

I. Lucio-Martinez, P. Chan, X. Mo, S. Hosier, and W. Tittel, “Proof-of-concept of real-world quantum key distribution with quantum frames,” New J. Phys. 11(9), 095001 (2009).
[Crossref]

Nam, S. W.

Nauerth, S.

Nolan, D.

Oblak, D.

Pan, J.-W.

Q. Zhang, F. Xu, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Large scale quantum key distribution: challenges and solutions [invited],” Opt. Express 26(18), 24260–24273 (2018).
[Crossref]

Peev, M.

Pelc, J. S.

Peng, C.-Z.

Q. Zhang, F. Xu, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Large scale quantum key distribution: challenges and solutions [invited],” Opt. Express 26(18), 24260–24273 (2018).
[Crossref]

Penty, R.

Qi, B.

H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108(13), 130503 (2012).
[Crossref]

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).
[Crossref]

C.-H. F. Fung, B. Qi, K. Tamaki, and H.-K. Lo, “Phase-remapping attack in practical quantum-key-distribution systems,” Phys. Rev. A 75(3), 032314 (2007).
[Crossref]

Y. Zhao, B. Qi, and H.-K. Lo, “Experimental quantum key distribution with active phase randomization,” Appl. Phys. Lett. 90(4), 044106 (2007).
[Crossref]

Qian, L.

Qin, X.

Rau, M.

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

Scarani, V.

Sharpe, A.

Shaw, M. D.

Shentu, G.-L.

Shields, A.

Shields, A. J.

Skaar, J.

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

Tam, S.-B.

Tamaki, K.

C.-H. F. Fung, B. Qi, K. Tamaki, and H.-K. Lo, “Phase-remapping attack in practical quantum-key-distribution systems,” Phys. Rev. A 75(3), 032314 (2007).
[Crossref]

Tang, Y.-L.

Tang, Z.

Temporão, G. P.

Tittel, W.

I. Lucio-Martinez, P. Chan, X. Mo, S. Hosier, and W. Tittel, “Proof-of-concept of real-world quantum key distribution with quantum frames,” New J. Phys. 11(9), 095001 (2009).
[Crossref]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

Valivarthi, R.

Verma, V. B.

Vitoreti, D.

von der Weid, J. P.

Wang, J.

Wang, L.-J.

Wang, X.

Wang, X.-B.

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]

Wang, Z.

Wei, Z.

Weier, H.

Weinfurter, H.

Wiechers, C.

Wittmann, C.

Xavier, G. B.

Xu, F.

Q. Zhang, F. Xu, Y.-A. Chen, C.-Z. Peng, and J.-W. Pan, “Large scale quantum key distribution: challenges and solutions [invited],” Opt. Express 26(18), 24260–24273 (2018).
[Crossref]

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).
[Crossref]

Yang, D.-X.

Yin, H.-L.

You, L.-X.

Yu, Z.-W.

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]

Yuan, Z.

Yuan, Z. L.

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

Zhang, L.

Zhang, Q.

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Fig. 1. A typical MDI-QKD scheme. WCP, weak coherent pulse; IM, intensity modulator; BS, beam splitter; PBS, polarization beam splitter; D1H, D1V, D2H, and D2V, four single photon detectors; BSM, Bell state measurement.

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Fig. 2. (a) Schematic of the proposed MDI-QKD system. LD, laser diode; CIR, optical circulator; IM, intensity modulator; Pol-M, polarization modulator; ATT, attenuator; PC, manual polarization controller; QC, quantum channel; BS, beam splitter; PBS, polarization beam splitter; SPD, single photon detector; CC, coincidence counter; DG, delay generator; PG, electrical pulse generator; EATT, electrical attenuator. (b) Schematic of the Pol-M. PM, phase modulator; FM, Faraday mirror; OPM, optical power meter.

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Fig. 3. (a) the variation of PER over time of the left-hand circular polarization state. (b) the variation of PER over time of the right-hand circular polarization state.

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Tables (3)

Table 1. Experimental values of the gain $Q_{Z}^{μ_{z}, μ_{z}}$ and quantum bit error rate (QBER) $E_{Z}^{μ_{z}, μ_{z}}$ in the diagonal (Z) basis.

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Table 2. Experimental values of gains $Q_{X}^{μ_{i}, μ_{j}}$ and QBERs $E_{X}^{μ_{i}, μ_{j}}$ in the circular (X) basis. Since there is only one electrical pulse generator (PG3) driving two Pol-Ms, when Alice modulates the right-hand circular polarization state (the voltage of $3 V_{π} / 2$ is required), Bob can only simultaneously generate a voltage close to $3 V_{π} / 2$ , not exactly $3 V_{π} / 2$ , and vice versa. As a result, we obtain fewer coincidence counts than those obtained by simultaneous modulation of the left-hand circular polarization state, resulting in slightly higher QBERs.

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Table 3. Parameters used to extract the lower bound of the secure key rate.

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Equations (14)

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| P_{o u t} ⟩ = {\hat{P}}_{P M U} | P_{i n} ⟩

| ψ_{1} ⟩ = \cos θ | e_{x}^{^{'}} ⟩ + e^{i φ} \sin θ | e_{y}^{^{'}} ⟩

| ψ_{2} ⟩ = e^{i φ_{e}} \cos θ | e_{x}^{^{'}} ⟩ + e^{i φ_{o}} e^{i φ} \sin θ | e_{y}^{^{'}} ⟩

{\hat{P}}_{F M} = | e_{x} ⟩ ⟨ e_{y} | + | e_{y} ⟩ ⟨ e_{x} |

\begin{aligned} | ψ_{3} ⟩ & = e^{i φ_{o}} e^{i φ_{e}} e^{i φ} \sin θ | e_{x}^{^{'}} ⟩ + e^{i φ_{e}} e^{i φ_{o}} \cos θ | e_{y}^{^{'}} ⟩ \\ = e^{i (φ_{e} + φ_{o})} (e^{i φ} \sin θ | e_{x}^{^{'}} ⟩ + \cos θ | e_{y}^{^{'}} ⟩) \end{aligned}

| ψ_{4} ⟩ = e^{i (φ_{e} + φ_{o})} | e_{x} ⟩

| ψ_{5} ⟩ = e^{i (φ_{e} + φ_{o})} | e_{y} ⟩

| ψ_{6} ⟩ = e^{i (φ_{e} + φ_{o})} | e_{x} ⟩

| ψ_{7} ⟩ = | e_{y} ⟩

| P_{o u t} ⟩ = \frac{\sqrt{2}}{2} e^{i (φ_{e} + φ_{o})} | e_{x} ⟩ + \frac{\sqrt{2}}{2} | e_{y} ⟩

| ψ^{^{'}} ⟩ = e^{i φ_{o}} | e_{y} ⟩

| P_{o u t}^{^{'}} ⟩ = \frac{\sqrt{2}}{2} e^{i φ_{o}} | e_{x} ⟩ + \frac{\sqrt{2}}{2} | e_{y} ⟩

E_{d} = \frac{1}{2} {\frac{1}{4} [(α_{1} + β_{1}) (α_{2} - β_{2}) + (α_{1} - β_{1}) (α_{2} + β_{2})] + \frac{1}{2} (α_{1} + β_{1}) (α_{1} - β_{1})}

R \geq p {p_{11} Y_{Z}^{11} [1 - H (E_{X}^{11})] - f Q_{Z}^{μ_{z}, μ_{z}} H (E_{Z}^{μ_{z}, μ_{z}})}

Diagonal (Z) basis
$Q_{Z}^{μ_{z}, μ_{z}}$	$E_{Z}^{μ_{z}, μ_{z}}$
$1.74 \times 10^{- 4}$	0.0149

Circular (X) basis
$I_{A}$	$I_{B}$	$Q_{X}^{μ_{i}, μ_{j}}$	$E_{x}^{μ_{i}, μ_{j}}$
$μ_{x}$	$μ_{x}$	$3.03 \times 10^{- 6}$	0.343
$μ_{x}$	$μ_{y}$	$2.15 \times 10^{- 5}$	0.416
$μ_{x}$	0	$8.18 \times 10^{- 7}$	0.497
$μ_{y}$	$μ_{x}$	$2.07 \times 10^{- 5}$	0.403
$μ_{y}$	$μ_{y}$	$5.25 \times 10^{- 5}$	0.332
$μ_{y}$	0	$1.44 \times 10^{- 5}$	0.489
0	$μ_{x}$	$8.53 \times 10^{- 7}$	0.496
0	$μ_{y}$	$1.51 \times 10^{- 5}$	0.479
0	0	0	0.500

Diagonal (Z) basis
$Q_{Z}^{μ_{z}, μ_{z}}$	$E_{Z}^{μ_{z}, μ_{z}}$
$1.74 \times 10^{- 4}$	0.0149

Circular (X) basis
$I_{A}$	$I_{B}$	$Q_{X}^{μ_{i}, μ_{j}}$	$E_{x}^{μ_{i}, μ_{j}}$
$μ_{x}$	$μ_{x}$	$3.03 \times 10^{- 6}$	0.343
$μ_{x}$	$μ_{y}$	$2.15 \times 10^{- 5}$	0.416
$μ_{x}$	0	$8.18 \times 10^{- 7}$	0.497
$μ_{y}$	$μ_{x}$	$2.07 \times 10^{- 5}$	0.403
$μ_{y}$	$μ_{y}$	$5.25 \times 10^{- 5}$	0.332
$μ_{y}$	0	$1.44 \times 10^{- 5}$	0.489
0	$μ_{x}$	$8.53 \times 10^{- 7}$	0.496
0	$μ_{y}$	$1.51 \times 10^{- 5}$	0.479
0	0	0	0.500