Abstract

We consider a subcarrier wave quantum key distribution (QKD) system, where quantum encoding is carried out at weak sidebands generated around a coherent optical beam as a result of electro-optical phase modulation. We study security of two protocols, B92 and BB84, against one of the most powerful attacks for this class of systems, the collective beam-splitting attack. Our analysis includes the case of high modulation index, where the sidebands are essentially multimode. We demonstrate numerically and experimentally that a subcarrier wave QKD system with realistic parameters is capable of distributing cryptographic keys over large distances in presence of collective attacks. We also show that BB84 protocol modification with discrimination of only one state in each basis performs not worse than the original BB84 protocol in this class of QKD systems, thus significantly simplifying the development of cryptographic networks using the considered QKD technique.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
  29. N. J. Cerf, “Asymmetric quantum cloning in any dimension,” J. Mod. Opt. 47, 187–2009 (2000).
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    [Crossref]
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    [Crossref]
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    [Crossref]

2017 (4)

G. P. Miroshnichenko, A. D. Kiselev, A. I. Trifanov, and A. V. Gleim, “Algebraic approach to electro-optic modulation of light: Exactly solvable multimode quantum model,” J. Opt. Soc. Am. B: Opt. Phys.,  34, pp. 1177–1190 (2017).
[Crossref]

D. B. Horoshko, V. N. Chizhevsky, and S. Ya. Kilin, “Afterpulsing model based on the quasi-continuous distribution of deep levels in single-photon avalanche diodes,” J. Mod. Opt. 64, 191–195 (2017).
[Crossref]

A. N. Klimov, S. P. Kulik, S. N. Molotkov, and T. A. Potapova, “On a simple attack, limiting the range transmission of secret keys in a system of quantum cryptography based on coding in a sub-carrier frequency,” Laser Phys. Lett. 14, 035201 (2017).
[Crossref]

A. V. Gleim, V. V. Chistyakov, O. I. Bannik, V. I. Egorov, N. V. Buldakov, A. B. Vasilev, A. A. Gaidash, A. V. Kozubov, S. V. Smirnov, S. M. Kynev, S. E. Khoruzhnikov, S. A. Kozlov, and V. N. Vasilev, “Sideband quantum communication at 1 Mbit/s on a metropolitan area network,” J. Opt. Technol. 84(6), 362–367 (2017).
[Crossref]

2016 (3)

A. V. Gleim, V. I. Egorov, Yu. V. Nazarov, S. V. Smirnov, V. V. Chistyakov, O. I. Bannik, A. A. Anisimov, S. M. Kynev, A. E. Ivanova, R. J. Collins, S. A. Kozlov, and G. S. Buller, “Secure polarization-independent subcarrier quantum key distribution in optical fiber channel using BB84 protocol with a strong reference,” Opt. Express 24, 2619–2633 (2016).
[Crossref] [PubMed]

A. Gaidash, A. Kozubov, V. Egorov, and A. Gleim, “Implementation of decoy states in a subcarrier wave quantum key distribution system,” J. Phys. Conf. Ser. 741, 012090 (2016).
[Crossref]

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

2015 (1)

M. Sasaki, M. Fujiwara, R.-B. Jin, M. Takeoka, T. S. Han, H. Endo, K.-I. Yoshino, T. Ochi, S. Asami, and A. Tajima, “Quantum photonic network: concept, basic tools, and future issues,” IEEE J. Sel. Top. Quantum Electron. 21, 6400313 (2015).
[Crossref]

2012 (2)

2010 (1)

J. Capmany and C. R. Fernandez-Pousa, “Quantum model for electro-optical phase modulation,” J. Opt. Soc. Am. B: Opt. Phys. 27, A119–A129 (2010).
[Crossref]

2009 (2)

K. Tamaki, N. Lütkenhaus, M. Koashi, and J. Batuwantudawe, “Unconditional security of the Bennett 1992 quantum-key-distribution scheme with a strong reference pulse,” Phys. Rev. A: At. Mol. Opt. Phys. 80, 032302 (2009).
[Crossref]

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

2007 (1)

D. Horoshko, S. Kilin, and M. Kolobov, “Asymmetric universal entangling machine,” Opt. Spectrosc. 103, 153–164 (2007).
[Crossref]

2005 (3)

O. Guerreau, F. J. Malassenet, S. W. McLaughlin, and J.-M. Merolla, “Quantum key distribution without a single-photon source using a strong reference,” IEEE Photonics Technol. Lett. 17, 1755–1757 (2005).
[Crossref]

H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
[Crossref] [PubMed]

I. Devetak and A. Winter, “Distillation of secret key and entanglement from quantum states,” Proc. R. Soc. London, Ser. A 461, 207–235 (2005).
[Crossref]

2004 (1)

M. Koashi, “Unconditional security of coherent-state quantum key distribution with a strong phase-reference pulse,” Phys. Rev. Lett. 93, 120501 (2004).
[Crossref] [PubMed]

2003 (1)

D. B. Horoshko and S. Ya. Kilin, “Optimal dimensionality for quantum cryptography,” Opt. Spectrosc. 94, 691–694 (2003).
[Crossref]

2002 (2)

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

J.-M. Merolla, L. Duraffourg, J.-P. Goedgebuer, A. Soujaeff, F. Patois, and W. T. Rhodes, “Integrated quantum key distribution system using single sideband detection,” Eur. Phys. J. D 18, 141–146 (2002).
[Crossref]

2000 (2)

N. J. Cerf, “Asymmetric quantum cloning in any dimension,” J. Mod. Opt. 47, 187–2009 (2000).
[Crossref]

P. W. Shor and J. Preskill, “Simple proof of security of the BB84 quantum key distribution protocol,” Phys. Rev. Lett. 85, 441 (2000).
[Crossref] [PubMed]

1999 (2)

J.-M. Merolla, Y. Mazurenko, J.-P. Goedgebuer, and W. T. Rhodes, “Single-photon interference in sidebands of phase-modulated light for quantum cryptography,” Phys. Rev. Lett. 82, 1656 (1999).
[Crossref]

J.-M. Merolla, Y. Mazurenko, J.-P. Goedgebuer, L. Duraffourg, H. Porte, and W. T. Rhodes, “Quantum cryptographic device using single-photon phase modulation,” Phys. Rev. A: At. Mol. Opt. Phys. 60, 1899 (1999).
[Crossref]

1998 (1)

D. Bruss, “Optimal eavesdropping in quantum cryptography with six states,” Phys. Rev. Lett. 81, 3018 (1998).
[Crossref]

1992 (2)

C. H. Bennett, F. Bessette, G. Brassard, and L. Savail, “Experimental quantum cryptography,” J. Cryptol. 5, 3–28 (1992).
[Crossref]

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68, 3121 (1992).
[Crossref] [PubMed]

Amaya, W.

Anisimov, A. A.

Asami, S.

M. Sasaki, M. Fujiwara, R.-B. Jin, M. Takeoka, T. S. Han, H. Endo, K.-I. Yoshino, T. Ochi, S. Asami, and A. Tajima, “Quantum photonic network: concept, basic tools, and future issues,” IEEE J. Sel. Top. Quantum Electron. 21, 6400313 (2015).
[Crossref]

Bannik, O. I.

Batuwantudawe, J.

K. Tamaki, N. Lütkenhaus, M. Koashi, and J. Batuwantudawe, “Unconditional security of the Bennett 1992 quantum-key-distribution scheme with a strong reference pulse,” Phys. Rev. A: At. Mol. Opt. Phys. 80, 032302 (2009).
[Crossref]

Bechmann-Pasquinucci, H.

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

Bennett, C. H.

C. H. Bennett, F. Bessette, G. Brassard, and L. Savail, “Experimental quantum cryptography,” J. Cryptol. 5, 3–28 (1992).
[Crossref]

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68, 3121 (1992).
[Crossref] [PubMed]

Bessette, F.

C. H. Bennett, F. Bessette, G. Brassard, and L. Savail, “Experimental quantum cryptography,” J. Cryptol. 5, 3–28 (1992).
[Crossref]

Brassard, G.

C. H. Bennett, F. Bessette, G. Brassard, and L. Savail, “Experimental quantum cryptography,” J. Cryptol. 5, 3–28 (1992).
[Crossref]

Bruss, D.

D. Bruss, “Optimal eavesdropping in quantum cryptography with six states,” Phys. Rev. Lett. 81, 3018 (1998).
[Crossref]

Buldakov, N. V.

Buller, G. S.

Calvo, D.

Capmany, J.

Cerf, N. J.

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

N. J. Cerf, “Asymmetric quantum cloning in any dimension,” J. Mod. Opt. 47, 187–2009 (2000).
[Crossref]

Chen, K.

H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
[Crossref] [PubMed]

Chistyakov, V. V.

Chizhevsky, V. N.

D. B. Horoshko, V. N. Chizhevsky, and S. Ya. Kilin, “Afterpulsing model based on the quasi-continuous distribution of deep levels in single-photon avalanche diodes,” J. Mod. Opt. 64, 191–195 (2017).
[Crossref]

Collins, R. J.

Cover, T. M.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, New-York, 1991).
[Crossref]

Curty, M.

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

Devetak, I.

I. Devetak and A. Winter, “Distillation of secret key and entanglement from quantum states,” Proc. R. Soc. London, Ser. A 461, 207–235 (2005).
[Crossref]

Diamanti, E.

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

Duraffourg, L.

J.-M. Merolla, L. Duraffourg, J.-P. Goedgebuer, A. Soujaeff, F. Patois, and W. T. Rhodes, “Integrated quantum key distribution system using single sideband detection,” Eur. Phys. J. D 18, 141–146 (2002).
[Crossref]

J.-M. Merolla, Y. Mazurenko, J.-P. Goedgebuer, L. Duraffourg, H. Porte, and W. T. Rhodes, “Quantum cryptographic device using single-photon phase modulation,” Phys. Rev. A: At. Mol. Opt. Phys. 60, 1899 (1999).
[Crossref]

Dusek, M.

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

Egorov, V.

A. Gaidash, A. Kozubov, V. Egorov, and A. Gleim, “Implementation of decoy states in a subcarrier wave quantum key distribution system,” J. Phys. Conf. Ser. 741, 012090 (2016).
[Crossref]

Egorov, V. I.

Endo, H.

M. Sasaki, M. Fujiwara, R.-B. Jin, M. Takeoka, T. S. Han, H. Endo, K.-I. Yoshino, T. Ochi, S. Asami, and A. Tajima, “Quantum photonic network: concept, basic tools, and future issues,” IEEE J. Sel. Top. Quantum Electron. 21, 6400313 (2015).
[Crossref]

Fernandez-Pousa, C. R.

J. Capmany and C. R. Fernandez-Pousa, “Quantum model for electro-optical phase modulation,” J. Opt. Soc. Am. B: Opt. Phys. 27, A119–A129 (2010).
[Crossref]

Fujiwara, M.

M. Sasaki, M. Fujiwara, R.-B. Jin, M. Takeoka, T. S. Han, H. Endo, K.-I. Yoshino, T. Ochi, S. Asami, and A. Tajima, “Quantum photonic network: concept, basic tools, and future issues,” IEEE J. Sel. Top. Quantum Electron. 21, 6400313 (2015).
[Crossref]

Gaidash, A.

A. Gaidash, A. Kozubov, V. Egorov, and A. Gleim, “Implementation of decoy states in a subcarrier wave quantum key distribution system,” J. Phys. Conf. Ser. 741, 012090 (2016).
[Crossref]

Gaidash, A. A.

Garcia Munoz, V.

Gisin, N.

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

Gleim, A.

A. Gaidash, A. Kozubov, V. Egorov, and A. Gleim, “Implementation of decoy states in a subcarrier wave quantum key distribution system,” J. Phys. Conf. Ser. 741, 012090 (2016).
[Crossref]

Gleim, A. V.

Goedgebuer, J.-P.

J.-M. Merolla, L. Duraffourg, J.-P. Goedgebuer, A. Soujaeff, F. Patois, and W. T. Rhodes, “Integrated quantum key distribution system using single sideband detection,” Eur. Phys. J. D 18, 141–146 (2002).
[Crossref]

J.-M. Merolla, Y. Mazurenko, J.-P. Goedgebuer, L. Duraffourg, H. Porte, and W. T. Rhodes, “Quantum cryptographic device using single-photon phase modulation,” Phys. Rev. A: At. Mol. Opt. Phys. 60, 1899 (1999).
[Crossref]

J.-M. Merolla, Y. Mazurenko, J.-P. Goedgebuer, and W. T. Rhodes, “Single-photon interference in sidebands of phase-modulated light for quantum cryptography,” Phys. Rev. Lett. 82, 1656 (1999).
[Crossref]

Guerreau, O.

O. Guerreau, F. J. Malassenet, S. W. McLaughlin, and J.-M. Merolla, “Quantum key distribution without a single-photon source using a strong reference,” IEEE Photonics Technol. Lett. 17, 1755–1757 (2005).
[Crossref]

Han, T. S.

M. Sasaki, M. Fujiwara, R.-B. Jin, M. Takeoka, T. S. Han, H. Endo, K.-I. Yoshino, T. Ochi, S. Asami, and A. Tajima, “Quantum photonic network: concept, basic tools, and future issues,” IEEE J. Sel. Top. Quantum Electron. 21, 6400313 (2015).
[Crossref]

Holevo, A. S.

A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory, (North-Holland, Amsterdam, 1982).

Horoshko, D.

D. Horoshko, S. Kilin, and M. Kolobov, “Asymmetric universal entangling machine,” Opt. Spectrosc. 103, 153–164 (2007).
[Crossref]

Horoshko, D. B.

D. B. Horoshko, V. N. Chizhevsky, and S. Ya. Kilin, “Afterpulsing model based on the quasi-continuous distribution of deep levels in single-photon avalanche diodes,” J. Mod. Opt. 64, 191–195 (2017).
[Crossref]

D. B. Horoshko and S. Ya. Kilin, “Optimal dimensionality for quantum cryptography,” Opt. Spectrosc. 94, 691–694 (2003).
[Crossref]

Ivanova, A. E.

Jin, R.-B.

M. Sasaki, M. Fujiwara, R.-B. Jin, M. Takeoka, T. S. Han, H. Endo, K.-I. Yoshino, T. Ochi, S. Asami, and A. Tajima, “Quantum photonic network: concept, basic tools, and future issues,” IEEE J. Sel. Top. Quantum Electron. 21, 6400313 (2015).
[Crossref]

Khersonsky, V.K.

D. A. Varshalovich, A. N. Moskalev, and V.K. Khersonsky, Quantum Theory of Angular Momentum, (World Scientific, Singapore, 1988).
[Crossref]

Khoruzhnikov, S. E.

Kilin, S.

D. Horoshko, S. Kilin, and M. Kolobov, “Asymmetric universal entangling machine,” Opt. Spectrosc. 103, 153–164 (2007).
[Crossref]

Kilin, S. Ya.

D. B. Horoshko, V. N. Chizhevsky, and S. Ya. Kilin, “Afterpulsing model based on the quasi-continuous distribution of deep levels in single-photon avalanche diodes,” J. Mod. Opt. 64, 191–195 (2017).
[Crossref]

D. B. Horoshko and S. Ya. Kilin, “Optimal dimensionality for quantum cryptography,” Opt. Spectrosc. 94, 691–694 (2003).
[Crossref]

Kiselev, A. D.

G. P. Miroshnichenko, A. D. Kiselev, A. I. Trifanov, and A. V. Gleim, “Algebraic approach to electro-optic modulation of light: Exactly solvable multimode quantum model,” J. Opt. Soc. Am. B: Opt. Phys.,  34, pp. 1177–1190 (2017).
[Crossref]

Klimov, A. N.

A. N. Klimov, S. P. Kulik, S. N. Molotkov, and T. A. Potapova, “On a simple attack, limiting the range transmission of secret keys in a system of quantum cryptography based on coding in a sub-carrier frequency,” Laser Phys. Lett. 14, 035201 (2017).
[Crossref]

Koashi, M.

K. Tamaki, N. Lütkenhaus, M. Koashi, and J. Batuwantudawe, “Unconditional security of the Bennett 1992 quantum-key-distribution scheme with a strong reference pulse,” Phys. Rev. A: At. Mol. Opt. Phys. 80, 032302 (2009).
[Crossref]

M. Koashi, “Unconditional security of coherent-state quantum key distribution with a strong phase-reference pulse,” Phys. Rev. Lett. 93, 120501 (2004).
[Crossref] [PubMed]

Kolobov, M.

D. Horoshko, S. Kilin, and M. Kolobov, “Asymmetric universal entangling machine,” Opt. Spectrosc. 103, 153–164 (2007).
[Crossref]

Kozlov, S. A.

Kozubov, A.

A. Gaidash, A. Kozubov, V. Egorov, and A. Gleim, “Implementation of decoy states in a subcarrier wave quantum key distribution system,” J. Phys. Conf. Ser. 741, 012090 (2016).
[Crossref]

Kozubov, A. V.

Kulik, S. P.

A. N. Klimov, S. P. Kulik, S. N. Molotkov, and T. A. Potapova, “On a simple attack, limiting the range transmission of secret keys in a system of quantum cryptography based on coding in a sub-carrier frequency,” Laser Phys. Lett. 14, 035201 (2017).
[Crossref]

Kynev, S. M.

Lo, H.-K.

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

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

H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
[Crossref] [PubMed]

Lütkenhaus, N.

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

K. Tamaki, N. Lütkenhaus, M. Koashi, and J. Batuwantudawe, “Unconditional security of the Bennett 1992 quantum-key-distribution scheme with a strong reference pulse,” Phys. Rev. A: At. Mol. Opt. Phys. 80, 032302 (2009).
[Crossref]

Ma, X.

H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
[Crossref] [PubMed]

Malassenet, F. J.

O. Guerreau, F. J. Malassenet, S. W. McLaughlin, and J.-M. Merolla, “Quantum key distribution without a single-photon source using a strong reference,” IEEE Photonics Technol. Lett. 17, 1755–1757 (2005).
[Crossref]

Mandel, L.

L. Mandel and E. Wolf, Optical coherence and quantum optics, (Cambridge University, 1995).
[Crossref]

Martinez, A.

Mazurenko, Y.

J.-M. Merolla, Y. Mazurenko, J.-P. Goedgebuer, and W. T. Rhodes, “Single-photon interference in sidebands of phase-modulated light for quantum cryptography,” Phys. Rev. Lett. 82, 1656 (1999).
[Crossref]

J.-M. Merolla, Y. Mazurenko, J.-P. Goedgebuer, L. Duraffourg, H. Porte, and W. T. Rhodes, “Quantum cryptographic device using single-photon phase modulation,” Phys. Rev. A: At. Mol. Opt. Phys. 60, 1899 (1999).
[Crossref]

McLaughlin, S. W.

O. Guerreau, F. J. Malassenet, S. W. McLaughlin, and J.-M. Merolla, “Quantum key distribution without a single-photon source using a strong reference,” IEEE Photonics Technol. Lett. 17, 1755–1757 (2005).
[Crossref]

Merolla, J.-M.

O. Guerreau, F. J. Malassenet, S. W. McLaughlin, and J.-M. Merolla, “Quantum key distribution without a single-photon source using a strong reference,” IEEE Photonics Technol. Lett. 17, 1755–1757 (2005).
[Crossref]

J.-M. Merolla, L. Duraffourg, J.-P. Goedgebuer, A. Soujaeff, F. Patois, and W. T. Rhodes, “Integrated quantum key distribution system using single sideband detection,” Eur. Phys. J. D 18, 141–146 (2002).
[Crossref]

J.-M. Merolla, Y. Mazurenko, J.-P. Goedgebuer, L. Duraffourg, H. Porte, and W. T. Rhodes, “Quantum cryptographic device using single-photon phase modulation,” Phys. Rev. A: At. Mol. Opt. Phys. 60, 1899 (1999).
[Crossref]

J.-M. Merolla, Y. Mazurenko, J.-P. Goedgebuer, and W. T. Rhodes, “Single-photon interference in sidebands of phase-modulated light for quantum cryptography,” Phys. Rev. Lett. 82, 1656 (1999).
[Crossref]

Miroshnichenko, G. P.

G. P. Miroshnichenko, A. D. Kiselev, A. I. Trifanov, and A. V. Gleim, “Algebraic approach to electro-optic modulation of light: Exactly solvable multimode quantum model,” J. Opt. Soc. Am. B: Opt. Phys.,  34, pp. 1177–1190 (2017).
[Crossref]

Molotkov, S. N.

A. N. Klimov, S. P. Kulik, S. N. Molotkov, and T. A. Potapova, “On a simple attack, limiting the range transmission of secret keys in a system of quantum cryptography based on coding in a sub-carrier frequency,” Laser Phys. Lett. 14, 035201 (2017).
[Crossref]

Mora, J.

Moskalev, A. N.

D. A. Varshalovich, A. N. Moskalev, and V.K. Khersonsky, Quantum Theory of Angular Momentum, (World Scientific, Singapore, 1988).
[Crossref]

Nazarov, Yu. V.

Ochi, T.

M. Sasaki, M. Fujiwara, R.-B. Jin, M. Takeoka, T. S. Han, H. Endo, K.-I. Yoshino, T. Ochi, S. Asami, and A. Tajima, “Quantum photonic network: concept, basic tools, and future issues,” IEEE J. Sel. Top. Quantum Electron. 21, 6400313 (2015).
[Crossref]

Patois, F.

J.-M. Merolla, L. Duraffourg, J.-P. Goedgebuer, A. Soujaeff, F. Patois, and W. T. Rhodes, “Integrated quantum key distribution system using single sideband detection,” Eur. Phys. J. D 18, 141–146 (2002).
[Crossref]

Peev, M.

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

Porte, H.

J.-M. Merolla, Y. Mazurenko, J.-P. Goedgebuer, L. Duraffourg, H. Porte, and W. T. Rhodes, “Quantum cryptographic device using single-photon phase modulation,” Phys. Rev. A: At. Mol. Opt. Phys. 60, 1899 (1999).
[Crossref]

Potapova, T. A.

A. N. Klimov, S. P. Kulik, S. N. Molotkov, and T. A. Potapova, “On a simple attack, limiting the range transmission of secret keys in a system of quantum cryptography based on coding in a sub-carrier frequency,” Laser Phys. Lett. 14, 035201 (2017).
[Crossref]

Preskill, J.

P. W. Shor and J. Preskill, “Simple proof of security of the BB84 quantum key distribution protocol,” Phys. Rev. Lett. 85, 441 (2000).
[Crossref] [PubMed]

Qi, B.

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

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

Rhodes, W. T.

J.-M. Merolla, L. Duraffourg, J.-P. Goedgebuer, A. Soujaeff, F. Patois, and W. T. Rhodes, “Integrated quantum key distribution system using single sideband detection,” Eur. Phys. J. D 18, 141–146 (2002).
[Crossref]

J.-M. Merolla, Y. Mazurenko, J.-P. Goedgebuer, L. Duraffourg, H. Porte, and W. T. Rhodes, “Quantum cryptographic device using single-photon phase modulation,” Phys. Rev. A: At. Mol. Opt. Phys. 60, 1899 (1999).
[Crossref]

J.-M. Merolla, Y. Mazurenko, J.-P. Goedgebuer, and W. T. Rhodes, “Single-photon interference in sidebands of phase-modulated light for quantum cryptography,” Phys. Rev. Lett. 82, 1656 (1999).
[Crossref]

Ribordy, G.

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

Ruiz-Alba, A.

Sasaki, M.

M. Sasaki, M. Fujiwara, R.-B. Jin, M. Takeoka, T. S. Han, H. Endo, K.-I. Yoshino, T. Ochi, S. Asami, and A. Tajima, “Quantum photonic network: concept, basic tools, and future issues,” IEEE J. Sel. Top. Quantum Electron. 21, 6400313 (2015).
[Crossref]

Savail, L.

C. H. Bennett, F. Bessette, G. Brassard, and L. Savail, “Experimental quantum cryptography,” J. Cryptol. 5, 3–28 (1992).
[Crossref]

Scarani, V.

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

Scully, M. O.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).
[Crossref]

Shor, P. W.

P. W. Shor and J. Preskill, “Simple proof of security of the BB84 quantum key distribution protocol,” Phys. Rev. Lett. 85, 441 (2000).
[Crossref] [PubMed]

Smirnov, S. V.

Soujaeff, A.

J.-M. Merolla, L. Duraffourg, J.-P. Goedgebuer, A. Soujaeff, F. Patois, and W. T. Rhodes, “Integrated quantum key distribution system using single sideband detection,” Eur. Phys. J. D 18, 141–146 (2002).
[Crossref]

Tajima, A.

M. Sasaki, M. Fujiwara, R.-B. Jin, M. Takeoka, T. S. Han, H. Endo, K.-I. Yoshino, T. Ochi, S. Asami, and A. Tajima, “Quantum photonic network: concept, basic tools, and future issues,” IEEE J. Sel. Top. Quantum Electron. 21, 6400313 (2015).
[Crossref]

Takeoka, M.

M. Sasaki, M. Fujiwara, R.-B. Jin, M. Takeoka, T. S. Han, H. Endo, K.-I. Yoshino, T. Ochi, S. Asami, and A. Tajima, “Quantum photonic network: concept, basic tools, and future issues,” IEEE J. Sel. Top. Quantum Electron. 21, 6400313 (2015).
[Crossref]

Tamaki, K.

K. Tamaki, N. Lütkenhaus, M. Koashi, and J. Batuwantudawe, “Unconditional security of the Bennett 1992 quantum-key-distribution scheme with a strong reference pulse,” Phys. Rev. A: At. Mol. Opt. Phys. 80, 032302 (2009).
[Crossref]

Thomas, J. A.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, New-York, 1991).
[Crossref]

Tittel, W.

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

Trifanov, A. I.

G. P. Miroshnichenko, A. D. Kiselev, A. I. Trifanov, and A. V. Gleim, “Algebraic approach to electro-optic modulation of light: Exactly solvable multimode quantum model,” J. Opt. Soc. Am. B: Opt. Phys.,  34, pp. 1177–1190 (2017).
[Crossref]

Varshalovich, D. A.

D. A. Varshalovich, A. N. Moskalev, and V.K. Khersonsky, Quantum Theory of Angular Momentum, (World Scientific, Singapore, 1988).
[Crossref]

Vasilev, A. B.

Vasilev, V. N.

Winter, A.

I. Devetak and A. Winter, “Distillation of secret key and entanglement from quantum states,” Proc. R. Soc. London, Ser. A 461, 207–235 (2005).
[Crossref]

Wolf, E.

L. Mandel and E. Wolf, Optical coherence and quantum optics, (Cambridge University, 1995).
[Crossref]

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New-York, 1984).

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New-York, 1984).

Yoshino, K.-I.

M. Sasaki, M. Fujiwara, R.-B. Jin, M. Takeoka, T. S. Han, H. Endo, K.-I. Yoshino, T. Ochi, S. Asami, and A. Tajima, “Quantum photonic network: concept, basic tools, and future issues,” IEEE J. Sel. Top. Quantum Electron. 21, 6400313 (2015).
[Crossref]

Yuan, Z.

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

Zbinden, H.

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

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).
[Crossref]

Eur. Phys. J. D (1)

J.-M. Merolla, L. Duraffourg, J.-P. Goedgebuer, A. Soujaeff, F. Patois, and W. T. Rhodes, “Integrated quantum key distribution system using single sideband detection,” Eur. Phys. J. D 18, 141–146 (2002).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

M. Sasaki, M. Fujiwara, R.-B. Jin, M. Takeoka, T. S. Han, H. Endo, K.-I. Yoshino, T. Ochi, S. Asami, and A. Tajima, “Quantum photonic network: concept, basic tools, and future issues,” IEEE J. Sel. Top. Quantum Electron. 21, 6400313 (2015).
[Crossref]

IEEE Photonics Technol. Lett. (1)

O. Guerreau, F. J. Malassenet, S. W. McLaughlin, and J.-M. Merolla, “Quantum key distribution without a single-photon source using a strong reference,” IEEE Photonics Technol. Lett. 17, 1755–1757 (2005).
[Crossref]

J. Cryptol. (1)

C. H. Bennett, F. Bessette, G. Brassard, and L. Savail, “Experimental quantum cryptography,” J. Cryptol. 5, 3–28 (1992).
[Crossref]

J. Mod. Opt. (2)

D. B. Horoshko, V. N. Chizhevsky, and S. Ya. Kilin, “Afterpulsing model based on the quasi-continuous distribution of deep levels in single-photon avalanche diodes,” J. Mod. Opt. 64, 191–195 (2017).
[Crossref]

N. J. Cerf, “Asymmetric quantum cloning in any dimension,” J. Mod. Opt. 47, 187–2009 (2000).
[Crossref]

J. Opt. Soc. Am. B: Opt. Phys. (2)

G. P. Miroshnichenko, A. D. Kiselev, A. I. Trifanov, and A. V. Gleim, “Algebraic approach to electro-optic modulation of light: Exactly solvable multimode quantum model,” J. Opt. Soc. Am. B: Opt. Phys.,  34, pp. 1177–1190 (2017).
[Crossref]

J. Capmany and C. R. Fernandez-Pousa, “Quantum model for electro-optical phase modulation,” J. Opt. Soc. Am. B: Opt. Phys. 27, A119–A129 (2010).
[Crossref]

J. Opt. Technol. (1)

J. Phys. Conf. Ser. (1)

A. Gaidash, A. Kozubov, V. Egorov, and A. Gleim, “Implementation of decoy states in a subcarrier wave quantum key distribution system,” J. Phys. Conf. Ser. 741, 012090 (2016).
[Crossref]

Laser Phys. Lett. (1)

A. N. Klimov, S. P. Kulik, S. N. Molotkov, and T. A. Potapova, “On a simple attack, limiting the range transmission of secret keys in a system of quantum cryptography based on coding in a sub-carrier frequency,” Laser Phys. Lett. 14, 035201 (2017).
[Crossref]

NPJ Quantum. Inf. (1)

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

Opt. Express (2)

Opt. Spectrosc. (2)

D. B. Horoshko and S. Ya. Kilin, “Optimal dimensionality for quantum cryptography,” Opt. Spectrosc. 94, 691–694 (2003).
[Crossref]

D. Horoshko, S. Kilin, and M. Kolobov, “Asymmetric universal entangling machine,” Opt. Spectrosc. 103, 153–164 (2007).
[Crossref]

Phys. Rev. A: At. Mol. Opt. Phys. (2)

J.-M. Merolla, Y. Mazurenko, J.-P. Goedgebuer, L. Duraffourg, H. Porte, and W. T. Rhodes, “Quantum cryptographic device using single-photon phase modulation,” Phys. Rev. A: At. Mol. Opt. Phys. 60, 1899 (1999).
[Crossref]

K. Tamaki, N. Lütkenhaus, M. Koashi, and J. Batuwantudawe, “Unconditional security of the Bennett 1992 quantum-key-distribution scheme with a strong reference pulse,” Phys. Rev. A: At. Mol. Opt. Phys. 80, 032302 (2009).
[Crossref]

Phys. Rev. Lett. (7)

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68, 3121 (1992).
[Crossref] [PubMed]

J.-M. Merolla, Y. Mazurenko, J.-P. Goedgebuer, and W. T. Rhodes, “Single-photon interference in sidebands of phase-modulated light for quantum cryptography,” Phys. Rev. Lett. 82, 1656 (1999).
[Crossref]

M. Koashi, “Unconditional security of coherent-state quantum key distribution with a strong phase-reference pulse,” Phys. Rev. Lett. 93, 120501 (2004).
[Crossref] [PubMed]

D. Bruss, “Optimal eavesdropping in quantum cryptography with six states,” Phys. Rev. Lett. 81, 3018 (1998).
[Crossref]

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

H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005).
[Crossref] [PubMed]

P. W. Shor and J. Preskill, “Simple proof of security of the BB84 quantum key distribution protocol,” Phys. Rev. Lett. 85, 441 (2000).
[Crossref] [PubMed]

Proc. R. Soc. London, Ser. A (1)

I. Devetak and A. Winter, “Distillation of secret key and entanglement from quantum states,” Proc. R. Soc. London, Ser. A 461, 207–235 (2005).
[Crossref]

Rev. Mod. Phys (2)

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

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

Other (6)

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).
[Crossref]

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, New-York, 1991).
[Crossref]

D. A. Varshalovich, A. N. Moskalev, and V.K. Khersonsky, Quantum Theory of Angular Momentum, (World Scientific, Singapore, 1988).
[Crossref]

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New-York, 1984).

A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory, (North-Holland, Amsterdam, 1982).

L. Mandel and E. Wolf, Optical coherence and quantum optics, (Cambridge University, 1995).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Schematic diagram of the SCW QKD setup. PSM is an electro-optical phase shift modulator; SF is a spectral filter that blocks light at the central frequency; SPD is a single photon detector. Diagrams in circles show the spectra in the corresponding parts of the setup. Only two sidebands are shown in the spectra for simplicity.
Fig. 2
Fig. 2 Diagrams of (a) a binary symmetric error and erasure channel and (b) an equivalent cascade of a symmetric binary channel and an erasure channel. Question mark denotes the inconclusive result.
Fig. 3
Fig. 3 QBER dependence on the channel loss in the SCW QKD system with experimental parameters presented in Sec. 3. Two lines correspond to two different detectors employed on Bob’s side.
Fig. 4
Fig. 4 Mean photon number providing the maximum value of the secret key rate as a function of channel loss for two types of photodetectors. Optimization is performed for BB84-OSD protocol in the presence of the CBS attack.
Fig. 5
Fig. 5 Secure key rate dependence on channel loss in the SCW QKD system with parameters given in Sec. 3 using two types of photodetectors. Optimization is performed for BB84-OSD protocol in the presence of the CBS attack. Secure key generation rate K is calculated from Eq. (29) for the optimal values of μ shown in Fig. 4.
Fig. 6
Fig. 6 Experimental sifted key rate (a) and quantum bit error rate (b) as functions of the channel loss in the SCW QKD system with APD implementing the BB84-OSD protocol.
Fig. 7
Fig. 7 Experimental secure key rate dependence on channel loss in the SCW QKD system with APD, implementing the BB84-OSD protocol.

Equations (40)

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

K = ν S P B [ 1 leak EC ( Q ) max E χ ( A : E ) ] ,
χ ( A : E ) = S ( ρ ) k p k S ( ρ k ) ,
C = 1 G ( 1 G ) log 2 ( 1 G ) + E log 2 ( E ) + ( 1 G E ) log 2 ( 1 G E ) .
| ψ 0 ( φ A ) = k = S S | α k ( φ A ) k ,
α k ( φ A ) = μ 0 d 0 k S ( β ) e i ( θ 1 + φ A ) k ,
cos ( β ) = 1 1 2 ( m S + 0.5 ) 2 .
d n k S ( β ) S J n k ( m ) ,
| ψ L ( φ A ) = k = S S | η ( L ) α k ( φ A ) k .
| ψ B ( φ A , φ ) = k = S S | α k ( φ A , φ ) k ,
α k ( φ A , φ ) = μ 0 η ( L ) exp ( i θ 2 k ) d 0 k S ( β ) ,
cos β = cos 2 β sin 2 β cos ( φ A φ + φ 0 ) ,
α ¯ k ( φ A , φ B ) = μ 0 η ( L ) η B exp ( i θ 2 k ) d 0 k S ( β ) .
n ph ( φ A , φ B ) = ϑ | α ¯ 0 ( φ A , φ B ) | 2 + k 0 | α ¯ k ( φ A , φ B ) | 2 = μ 0 η ( L ) η B ( 1 ( 1 ϑ ) | d 00 S ( β ) | 2 ) ,
k = S S d n k S ( β ) ( d l k S ( β ) ) * = δ n l ,
P det ( φ A , φ B ) = ( η D n ph ( φ A , φ B ) T + γ dark ) Δ t ,
E = 1 2 P det ( 0 , π + Δ φ ) ,
1 E G = 1 2 P det ( 0 , Δ φ ) ,
Q ( L ) = 1 ( 1 ϑ ) | d 00 S ( β 0 ) | 2 + ζ ( L ) 2 ( 1 ϑ ) | d 00 S ( β 0 ) | 2 ( 1 ϑ ) | d 00 S ( β 1 ) | 2 + 2 ζ ( L ) ,
| ψ E ( φ A ) = k = S S | η ¯ ( L ) α k ( φ A ) k ,
U = exp ( i π 2 k = S S k a k a k ) ,
ρ = 1 2 | ψ E ( 0 ) ψ E ( 0 ) | + 1 2 | ψ E ( π ) ψ E ( π ) | .
λ 1 , 2 = 1 2 ( 1 ± | I ( 0 , π ) | ) ,
I ( φ 1 , φ 2 ) = ψ E ( φ 1 ) | ψ E ( φ 2 ) = k = S S η ¯ ( L ) α k ( φ 1 ) | η ¯ ( L ) α k ( φ 2 ) k k
α | β = exp ( 1 2 ( | α | 2 + | β | 2 ) + α * β )
I ( φ 1 , φ 2 ) = exp [ η ¯ ( L ) 2 k = S S ( | α k ( φ 1 ) | 2 + | α k ( φ 2 ) | 2 2 α k * ( φ 1 ) α k ( φ 2 ) ) ] = exp [ μ 0 η ¯ ( L ) k = S S | d 0 k S ( β ) | 2 ( 1 e i ( φ 1 φ 2 ) k ) ] ,
k = S S | d 0 k S ( β ) | 2 ( 1 e i ( φ 1 φ 2 ) k ) = 1 d 00 S ( β ) ,
cos ( β ) = cos 2 ( β ) + sin 2 ( β ) cos ( φ 1 φ 2 ) .
I ( φ 1 , φ 2 ) = exp [ μ 0 η ¯ ( L ) ( 1 d 00 S ( β ) ) ] .
χ ( A : E ) = h ( 1 2 ( 1 exp [ μ 0 η ¯ ( L ) ( 1 d 00 S ( 2 β ) ) ] ) .
K ( μ 0 , m , L ) = 1 G 2 T [ 1 h ( E 1 G ) h ( 1 2 ( 1 e μ 0 η ¯ ( L ) ( 1 J 0 ( 2 m ) ) ) ] ,
μ ( μ 0 , m ) = k 0 | α k ( φ A ) | 2 = μ 0 ( 1 | d 00 S ( β ) | 2 ) μ 0 ( 1 J 0 ( m ) 2 ) ,
D ( 0 ) | ψ L ( 0 ) = | μ s + | μ s | μ ¯ c 0 ,
D ( 0 ) | ψ L ( π ) = | vac + | vac | μ ¯ 0 ,
| μ s + = k = 1 S | α k ( 0 , φ 0 ) k ,
| μ s = k = S 1 | α k ( 0 , φ 0 ) k ,
D ( 0 ) | ψ L ( 0 ) = | μ s + | vac | μ ¯ c 0 ,
D ( 0 ) | ψ L ( π ) = | vac + | μ s | μ ¯ c 0 ,
ψ L ( π ) | D ( 0 ) D ( 0 ) | ψ L ( 0 ) = ψ L ( π ) | D ( 0 ) D ( 0 ) | ψ L ( 0 ) ,
exp { μ s 1 2 ( μ ¯ μ ¯ c ) 2 } = exp { μ s } ,
μ s = μ s + 1 2 ( μ ¯ μ ¯ 2 μ s ) 2 μ s + μ s 2 2 μ ¯ .

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