Skip to main content
Erschienen in: Quantum Information Processing 5/2016

01.05.2016

Security of a semi-quantum protocol where reflections contribute to the secret key

verfasst von: Walter O. Krawec

Erschienen in: Quantum Information Processing | Ausgabe 5/2016

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this paper, we provide a proof of unconditional security for a semi-quantum key distribution protocol introduced in a previous work. This particular protocol demonstrated the possibility of using X basis states to contribute to the raw key of the two users (as opposed to using only direct measurement results) even though a semi-quantum participant cannot directly manipulate such states. In this work, we provide a complete proof of security by deriving a lower bound of the protocol’s key rate in the asymptotic scenario. Using this bound, we are able to find an error threshold value such that for all error rates less than this threshold, it is guaranteed that A and B may distill a secure secret key; for error rates larger than this threshold, A and B should abort. We demonstrate that this error threshold compares favorably to several fully quantum protocols. We also comment on some interesting observations about the behavior of this protocol under certain noise scenarios.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, vol. 175. New York (1984) Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, vol. 175. New York (1984)
3.
Zurück zum Zitat Acin, A., Gisin, N., Scarani, V.: Coherent-pulse implementations of quantum cryptography protocols resistant to photon-number-splitting attacks. Phys. Rev. A 69, 012309 (2004)ADSCrossRef Acin, A., Gisin, N., Scarani, V.: Coherent-pulse implementations of quantum cryptography protocols resistant to photon-number-splitting attacks. Phys. Rev. A 69, 012309 (2004)ADSCrossRef
4.
Zurück zum Zitat Fung, C.-H.F., Lo, H.-K.: Security proof of a three-state quantum-key-distribution protocol without rotational symmetry. Phys. Rev. A 74, 042342 (2006)ADSCrossRef Fung, C.-H.F., Lo, H.-K.: Security proof of a three-state quantum-key-distribution protocol without rotational symmetry. Phys. Rev. A 74, 042342 (2006)ADSCrossRef
5.
Zurück zum Zitat Scarani, V., Bechmann-Pasquinucci, H., Cerf, N.J., Dušek, M., Lütkenhaus, N., Peev, M.: The security of practical quantum key distribution. Rev. Mod. Phys. 81, 1301–1350 (2009)ADSCrossRef Scarani, V., Bechmann-Pasquinucci, H., Cerf, N.J., Dušek, M., Lütkenhaus, N., Peev, M.: The security of practical quantum key distribution. Rev. Mod. Phys. 81, 1301–1350 (2009)ADSCrossRef
6.
Zurück zum Zitat Boyer, M., Kenigsberg, D., Mor, T.: Quantum key distribution with classical bob. In: First International Conference on Quantum, Nano, and Micro Technologies, 2007. ICQNM ’07, pp. 10–10 (2007) Boyer, M., Kenigsberg, D., Mor, T.: Quantum key distribution with classical bob. In: First International Conference on Quantum, Nano, and Micro Technologies, 2007. ICQNM ’07, pp. 10–10 (2007)
8.
Zurück zum Zitat Jian, W., Sheng, Z., Quan, Z., Chao-Jing, T.: Semiquantum key distribution using entangled states. Chin. Phys. Lett. 28(10), 100301 (2011)CrossRef Jian, W., Sheng, Z., Quan, Z., Chao-Jing, T.: Semiquantum key distribution using entangled states. Chin. Phys. Lett. 28(10), 100301 (2011)CrossRef
9.
Zurück zum Zitat Yu, K.-F., Yang, C.-W., Liao, C.-H., Hwang, T.: Authenticated semi-quantum key distribution protocol using bell states. Quantum Inf. Process. 13(6), 1457–1465 (2014) Yu, K.-F., Yang, C.-W., Liao, C.-H., Hwang, T.: Authenticated semi-quantum key distribution protocol using bell states. Quantum Inf. Process. 13(6), 1457–1465 (2014)
10.
Zurück zum Zitat Zou, X., Qiu, D., Li, L., Lihua, W., Li, L.: Semiquantum-key distribution using less than four quantum states. Phys. Rev. A 79, 052312 (2009)ADSCrossRef Zou, X., Qiu, D., Li, L., Lihua, W., Li, L.: Semiquantum-key distribution using less than four quantum states. Phys. Rev. A 79, 052312 (2009)ADSCrossRef
11.
Zurück zum Zitat Xian-Zhou, Z., Wei-Gui, G., Yong-Gang, T., Zhen-Zhong, R., Xiao-Tian, G.: Quantum key distribution series network protocol with m-classical bobs. Chin. Phys. B 18(6), 2143 (2009)ADSCrossRef Xian-Zhou, Z., Wei-Gui, G., Yong-Gang, T., Zhen-Zhong, R., Xiao-Tian, G.: Quantum key distribution series network protocol with m-classical bobs. Chin. Phys. B 18(6), 2143 (2009)ADSCrossRef
12.
Zurück zum Zitat Krawec, W.O.: Restricted attacks on semi-quantum key distribution protocols. Quantum Inf. Process. 13(11), 2417–2436 (2014)MathSciNetCrossRefMATH Krawec, W.O.: Restricted attacks on semi-quantum key distribution protocols. Quantum Inf. Process. 13(11), 2417–2436 (2014)MathSciNetCrossRefMATH
13.
Zurück zum Zitat Krawec, W.O.: Mediated semiquantum key distribution. Phys. Rev. A 91(3), 032323 (2015)ADSCrossRef Krawec, W.O.: Mediated semiquantum key distribution. Phys. Rev. A 91(3), 032323 (2015)ADSCrossRef
14.
Zurück zum Zitat Kun-Fei, Y., Yang, C.-W., Liao, C.-H., Hwang, T.: Authenticated semi-quantum key distribution protocol using bell states. Quantum Inf. Process. 13(6), 1457–1465 (2014)ADSMathSciNetCrossRef Kun-Fei, Y., Yang, C.-W., Liao, C.-H., Hwang, T.: Authenticated semi-quantum key distribution protocol using bell states. Quantum Inf. Process. 13(6), 1457–1465 (2014)ADSMathSciNetCrossRef
15.
Zurück zum Zitat Sun, Z.-W., Du, R.-G., Long, D.-Y.: Quantum key distribution with limited classical bob. Int. J. Quantum Inf. 11(1), 1350005 (2013) Sun, Z.-W., Du, R.-G., Long, D.-Y.: Quantum key distribution with limited classical bob. Int. J. Quantum Inf. 11(1), 1350005 (2013)
16.
Zurück zum Zitat Hua, L., Cai, Q.-Y.: Quantum key distribution with classical alice. Int. J. Quantum Inf. 6(06), 1195–1202 (2008)CrossRefMATH Hua, L., Cai, Q.-Y.: Quantum key distribution with classical alice. Int. J. Quantum Inf. 6(06), 1195–1202 (2008)CrossRefMATH
17.
Zurück zum Zitat Zou, X., Qiu, D., Zhang, S., Mateus, P.: Semiquantum key distribution without invoking the classical partys measurement capability. Quantum Inf. Process. 14(8), 2981–2996 (2015)ADSMathSciNetCrossRefMATH Zou, X., Qiu, D., Zhang, S., Mateus, P.: Semiquantum key distribution without invoking the classical partys measurement capability. Quantum Inf. Process. 14(8), 2981–2996 (2015)ADSMathSciNetCrossRefMATH
18.
Zurück zum Zitat Li, Q., Chan, W.H., Zhang, S.: Real semiquantum key distribution with secure delegated quantum computation. ArXiv preprint arXiv:1508.07090 (2015) Li, Q., Chan, W.H., Zhang, S.: Real semiquantum key distribution with secure delegated quantum computation. ArXiv preprint arXiv:​1508.​07090 (2015)
19.
Zurück zum Zitat Li, Q., Chan, W.H., Long, D.-Y.: Semiquantum secret sharing using entangled states. Phys. Rev. A 82, 022303 (2010)ADSCrossRef Li, Q., Chan, W.H., Long, D.-Y.: Semiquantum secret sharing using entangled states. Phys. Rev. A 82, 022303 (2010)ADSCrossRef
21.
Zurück zum Zitat Wang, J., Zhang, S., Zhang, Q., Tang, C.-J.: Semiquantum secret sharing using two-particle entangled state. Int. J. Quantum Inf. 10(5), 1250050 (2012) Wang, J., Zhang, S., Zhang, Q., Tang, C.-J.: Semiquantum secret sharing using two-particle entangled state. Int. J. Quantum Inf. 10(5), 1250050 (2012)
22.
Zurück zum Zitat Yang, C.-W., Hwang, T.: Efficient key construction on semi-quantum secret sharing protocols. Int. J. Quantum Inf. 11(5), 1350052 (2013) Yang, C.-W., Hwang, T.: Efficient key construction on semi-quantum secret sharing protocols. Int. J. Quantum Inf. 11(5), 1350052 (2013)
23.
Zurück zum Zitat Zou, X.F., Qiu, D.W.: Three-step semiquantum secure direct communication protocol. Sci. China Phys. Mech. Astron. 57(9), 1696–1702 (2014)ADSCrossRef Zou, X.F., Qiu, D.W.: Three-step semiquantum secure direct communication protocol. Sci. China Phys. Mech. Astron. 57(9), 1696–1702 (2014)ADSCrossRef
24.
Zurück zum Zitat Miyadera, T.: Relation between information and disturbance in quantum key distribution protocol with classical alice. Int. J. Quantum Inf. 9(6), 1427–1435 (2011) Miyadera, T.: Relation between information and disturbance in quantum key distribution protocol with classical alice. Int. J. Quantum Inf. 9(6), 1427–1435 (2011)
25.
Zurück zum Zitat Krawec, W.O.: Security Proof of a Semi-quantum Key Distribution Protocol. To appear: IEEE ISIT 2015; ArXiv preprint arXiv:1412.0282 (2015) Krawec, W.O.: Security Proof of a Semi-quantum Key Distribution Protocol. To appear: IEEE ISIT 2015; ArXiv preprint arXiv:​1412.​0282 (2015)
26.
Zurück zum Zitat Krawec, W.O.: Semi-Quantum Key Distribution. PhD thesis, Stevens Institute of Technology, May (2015) Krawec, W.O.: Semi-Quantum Key Distribution. PhD thesis, Stevens Institute of Technology, May (2015)
27.
29.
Zurück zum Zitat Briët, J., Harremoës, P.: Properties of classical and quantum Jensen–Shannon divergence. Phys. Rev. A 79(5), 052311 (2009)ADSCrossRef Briët, J., Harremoës, P.: Properties of classical and quantum Jensen–Shannon divergence. Phys. Rev. A 79(5), 052311 (2009)ADSCrossRef
30.
Zurück zum Zitat Renner, R., Gisin, N., Kraus, B.: Information-theoretic security proof for quantum-key-distribution protocols. Phys. Rev. A 72, 012332 (2005)ADSCrossRef Renner, R., Gisin, N., Kraus, B.: Information-theoretic security proof for quantum-key-distribution protocols. Phys. Rev. A 72, 012332 (2005)ADSCrossRef
31.
Zurück zum Zitat Krawec, W.O.: An Improved Asymptotic Key Rate Bound for a Mediated Semi-quantum Key Distribution Protocol. ArXiv preprint arXiv:1509.04797 (2015) Krawec, W.O.: An Improved Asymptotic Key Rate Bound for a Mediated Semi-quantum Key Distribution Protocol. ArXiv preprint arXiv:​1509.​04797 (2015)
32.
Zurück zum Zitat Watanabe, S., Matsumoto, R., Uyematsu, T.: Tomography increases key rates of quantum-key-distribution protocols. Phys. Rev. A 78(4), 042316 (2008)ADSCrossRef Watanabe, S., Matsumoto, R., Uyematsu, T.: Tomography increases key rates of quantum-key-distribution protocols. Phys. Rev. A 78(4), 042316 (2008)ADSCrossRef
33.
Zurück zum Zitat Kraus, B., Gisin, N., Renner, R.: Lower and upper bounds on the secret-key rate for quantum key distribution protocols using one-way classical communication. Phys. Rev. Lett. 95, 080501 (2005)ADSCrossRef Kraus, B., Gisin, N., Renner, R.: Lower and upper bounds on the secret-key rate for quantum key distribution protocols using one-way classical communication. Phys. Rev. Lett. 95, 080501 (2005)ADSCrossRef
34.
Zurück zum Zitat Devetak, I., Winter, A.: Distillation of secret key and entanglement from quantum states. Proc. R. Soc. A: Math. Phys. Eng. Sci. 461(2053), 207–235 (2005)ADSMathSciNetCrossRefMATH Devetak, I., Winter, A.: Distillation of secret key and entanglement from quantum states. Proc. R. Soc. A: Math. Phys. Eng. Sci. 461(2053), 207–235 (2005)ADSMathSciNetCrossRefMATH
35.
Zurück zum Zitat Christandl, M., Renner, R.: Artur Ekert. A Generic Security Proof for Quantum Key Distribution. ArXiv preprint quant-ph/0402131 (2004) Christandl, M., Renner, R.: Artur Ekert. A Generic Security Proof for Quantum Key Distribution. ArXiv preprint quant-ph/0402131 (2004)
36.
Zurück zum Zitat Christandl, M., Konig, R., Renner, R.: Postselection technique for quantum channels with applications to quantum cryptography. Phys. Rev. Lett. 102, 020504 (2009)ADSCrossRef Christandl, M., Konig, R., Renner, R.: Postselection technique for quantum channels with applications to quantum cryptography. Phys. Rev. Lett. 102, 020504 (2009)ADSCrossRef
37.
Zurück zum Zitat Renner, R.: Symmetry of large physical systems implies independence of subsystems. Nat. Phys. 3(9), 645–649 (2007)CrossRef Renner, R.: Symmetry of large physical systems implies independence of subsystems. Nat. Phys. 3(9), 645–649 (2007)CrossRef
38.
Zurück zum Zitat Matsumoto, R.: Improved asymptotic key rate of the B92 protocol. In: IEEE International Symposium on Information Theory Proceedings (ISIT), IEEE 2013, pp. 351–353 (2013) Matsumoto, R.: Improved asymptotic key rate of the B92 protocol. In: IEEE International Symposium on Information Theory Proceedings (ISIT), IEEE 2013, pp. 351–353 (2013)
39.
Zurück zum Zitat Branciard, C., Gisin, N., Lutkenhaus, N., Scarani, V.: Zero-error attacks and detection statistics in the coherent one-way protocol for quantum cryptography. Quantum Inf. Comput. 7(7), 639–664 (2007)MathSciNetMATH Branciard, C., Gisin, N., Lutkenhaus, N., Scarani, V.: Zero-error attacks and detection statistics in the coherent one-way protocol for quantum cryptography. Quantum Inf. Comput. 7(7), 639–664 (2007)MathSciNetMATH
Metadaten
Titel
Security of a semi-quantum protocol where reflections contribute to the secret key
verfasst von
Walter O. Krawec
Publikationsdatum
01.05.2016
Verlag
Springer US
Erschienen in
Quantum Information Processing / Ausgabe 5/2016
Print ISSN: 1570-0755
Elektronische ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-016-1266-3

Weitere Artikel der Ausgabe 5/2016

Quantum Information Processing 5/2016 Zur Ausgabe

Neuer Inhalt