Decoherence can help quantum cryptographic security

  • Vishal Sharma
  • U. Shrikant
  • R. SrikanthEmail author
  • Subhashish Banerjee


In quantum key distribution, one conservatively assumes that the eavesdropper Eve is restricted only by physical laws, whereas the legitimate parties, namely the sender Alice and receiver Bob, are subject to realistic constraints, such as noise due to environment-induced decoherence. In practice, Eve too may be bound by the limits imposed by noise, which can give rise to the possibility that decoherence works to the advantage of the legitimate parties. A particular scenario of this type is one where Eve can’t replace the noisy communication channel with an ideal one, but her eavesdropping channel itself remains noiseless. Here, we point out such a situation, where the security of the ping–pong protocol (modified to a key distribution scheme) against a noise-restricted adversary improves under a non-unital noisy channel, but deteriorates under unital channels. This highlights the surprising fact that, contrary to the conventional expectation, noise can be helpful to quantum information processing. Furthermore, we point out that the measurement outcome data in the context of the non-unital channel can’t be simulated by classical noise locally added by the legitimate users.


Ping–pong protocol QBER Entanglement QKD Quantum noise 



VS thanks the Ministry of Human Resource Development, Govt. of India, for offering a doctoral fellowship as a Ph.D. research scholar at Indian Institute of Technology Jodhpur, Rajasthan, India. SB thanks Atul Kumar and Anirban Pathak for useful discussions during the preliminary stage of this work. SB acknowledges support by the Project Number 03(1369)/16/EMR-II funded by Council of Scientific and Industrial Research, New Delhi, India. US and RS thank DST-SERB, Govt. of India, for financial support provided through the Project EMR/2016/004019.


  1. 1.
    Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74(1), 145 (2002)CrossRefzbMATHADSGoogle Scholar
  2. 2.
    Srinatha, N., Omkar, S., Srikanth, R., Banerjee, S., Pathak, A.: The quantum cryptographic switch. Quantum Inf. Process. 13, 1–12 (2014)CrossRefGoogle Scholar
  3. 3.
    Sharma, V.: Effect of noise on practical quantum communication systems. Def. Sci. J. 66(2), 186–192 (2016)CrossRefGoogle Scholar
  4. 4.
    Sharma, V., Shukla, C., Banerjee, S., Pathak, A.: Controlled bidirectional remote state preparation in noisy environment: a generalized view. Quantum Inf. Process. 14(9), 3441–3464 (2015)MathSciNetCrossRefzbMATHADSGoogle Scholar
  5. 5.
    Sharma, V., Thapliyal, K., Pathak, A., Banerjee, S.: A comparative study of protocols for secure quantum communication under noisy environment: single-qubit-based protocols versus entangled-state-based protocols. Quantum Inf. Process. 15(11), 4681–4710 (2016)MathSciNetCrossRefzbMATHADSGoogle Scholar
  6. 6.
    Sharma, V., Sharma, R.: Analysis of spread spectrum in MATLAB. Int. J. Sci. Eng. Res. 5(1), 1899–1902 (2014)Google Scholar
  7. 7.
    Wang, G., Shen, D., Chen, G., Pham, K., Blasch, E.: Polarization tracking for quantum satellite communications. In: Sensors and Systems for Space Applications VII, vol. 9085. International Society for Optics and Photonics, p. 90850T (2014)Google Scholar
  8. 8.
    Sharma, V., Banerjee, S.: Analysis of Atmospheric Effects on Satellite Based Quantum Communication: A Comparative Study (2017). arXiv:1711.08281
  9. 9.
    Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. Theor. Comput. Sci. 560(P1), 7–11 (1984)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Artur, K.E.: Quantum cryptography based on bells theorem. Phys. Rev. Lett. 67(6), 661 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Bannett, C.H.: Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68(21), 3121 (1992)MathSciNetCrossRefzbMATHADSGoogle Scholar
  12. 12.
    Goldenberg, L., Vaidman, L.: Quantum cryptography based on orthogonal states. Phys. Rev. Lett. 75(7), 1239 (1995)MathSciNetCrossRefzbMATHADSGoogle Scholar
  13. 13.
    Lo, H.-K., Chau, H.F.: Unconditional security of quantum key distribution over arbitrarily long distances. Science 283(5410), 2050–2056 (1999)CrossRefADSGoogle Scholar
  14. 14.
    Scarani, V., Gisin, N.: Quantum key distribution between N partners: optimal eavesdropping and bell’s inequalities. Phys. Rev. A 65, 012311 (2001)CrossRefADSGoogle Scholar
  15. 15.
    Lo, H.-K., Chau, H.F., Ardehali, M.: Efficient quantum key distribution scheme and a proof of its unconditional security. J. Cryptol. 18(2), 133–165 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    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(3), 1301 (2009)CrossRefADSGoogle Scholar
  17. 17.
    Pathak, A.: Elements of Quantum Computation and Quantum Communication. Taylor & Francis, Abingdon (2013)zbMATHGoogle Scholar
  18. 18.
    Shenoy-Hejamadi, A., Pathak, A., Radhakrishna, S.: Quantum cryptography: key distribution and beyond. Quanta 6(1), 1–47 (2017)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Deng, F.-G., Long, G.L.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69, 052319 (2004)CrossRefADSGoogle Scholar
  20. 20.
    Boström, K., Felbinger, T.: Deterministic secure direct communication using entanglement. Phys. Rev. Lett. 89(18), 187902 (2002)CrossRefADSGoogle Scholar
  21. 21.
    Lucamarini, M., Mancini, S.: Secure deterministic communication without entanglement. Phys. Rev. Lett. 94(14), 140501 (2005)CrossRefADSGoogle Scholar
  22. 22.
    Shukla, C., Pathak, A., Srikanth, R.: Beyond the Goldenberg-Vaidman protocol: Secure and eïňČcient quantum communication using arbitrary, orthogonal, multi-particle quantum states. Int. J. Quantum Inf. 10, 1241009 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Pappa, A., Chailloux, A., Diamanti, E., Kerenidis, I.: Practical quantum coin flipping. Phys. Rev. A 84, 052305 (2011)CrossRefADSGoogle Scholar
  24. 24.
    Amiri, R., Arrazola, J.M.: Quantum money with nearly optimal error tolerance. Phys. Rev. A 95(6), 062334 (2017)CrossRefADSGoogle Scholar
  25. 25.
    Wei, C.-Y., Cai, X.-Q., Liu, B., Wang, T., Gao, F.: A generic construction of quantum-oblivious-key-transfer-based private query with ideal database security and zero failure. IEEE Trans. Comput. 67, 2–8 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Shi, R-h, Yi, M., Zhong, H., Zhang, S., Cui, J.: Quantum private set intersection cardinality and its application to anonymous authentication. Inf. Sci. 370, 147–158 (2016)CrossRefGoogle Scholar
  27. 27.
    Banerjee, S., Srikanth, R.: Geometric phase of a qubit interacting with a squeezed-thermal bath. Eur. Phys. J. D Atom. Mol. Opt. Plasma Phys. 46(2), 335–344 (2008)MathSciNetGoogle Scholar
  28. 28.
    Srikanth, R., Banerjee, S.: Squeezed generalized amplitude damping channel. Phys. Rev. A 77(1), 012318 (2008)CrossRefADSGoogle Scholar
  29. 29.
    Ghosh, R.: Dynamics of decoherence without dissipation in a squeezed thermal bath. J. Phys. A: Math. Theor. 40(45), 13735 (2007)MathSciNetCrossRefzbMATHADSGoogle Scholar
  30. 30.
    Omkar, S., Srikanth, R., Banerjee, S.: Dissipative and non-dissipative single-qubit channels: dynamics and geometry. Quantum Inf. Process. 12(12), 3725–3744 (2013)MathSciNetCrossRefzbMATHADSGoogle Scholar
  31. 31.
    Adhikari, S., Home, D., Majumdar, A.S., Pan, A.K., Shenoy, A., Srikanth, R.: Toward secure communication using intra-particle entanglement. Quantum Inf. Process. 14(4), 1451–1468 (2015)CrossRefzbMATHADSGoogle Scholar
  32. 32.
    Renner, R., Gisin, N., Kraus, B.: Information-theoretic security proof for quantum-key-distribution protocols. Phys. Rev. A 72, 012332 (2005)CrossRefADSGoogle Scholar
  33. 33.
    Pirandola, S., García-Patrón, R., Braunstein, S.L., Lloyd, S.: Direct and reverse secret-key capacities of a quantum channel. Phys. Rev. Lett. 102, 050503 (2009)MathSciNetCrossRefADSGoogle Scholar
  34. 34.
    García-Patrón, R., Cerf, N.J.: Continuous-variable quantum key distribution protocols over noisy channels. Phys. Rev. Lett. 102, 130501 (2009)CrossRefADSGoogle Scholar
  35. 35.
    Subhashish Banerjee, R., Srikanth, C., Chandrashekar, M., Rungta, P.: Symmetry-noise interplay in a quantum walk on an \(n\)-cycle. Phys. Rev. A 78, 052316 (2008)CrossRefGoogle Scholar
  36. 36.
    Long, G-l, Deng, F-g, Wang, C., Li, X-h, Wen, K., Wang, W-y: Quantum secure direct communication and deterministic secure quantum communication. Front. Phys. China 2(3), 251–272 (2007)CrossRefADSGoogle Scholar
  37. 37.
    Wang, C., Deng, F.-G., Li, Y.-S., Liu, X.-S., Long, G.L.: Quantum secure direct communication with high-dimension quantum superdense coding. Phys. Rev. A 71(4), 044305 (2005)CrossRefADSGoogle Scholar
  38. 38.
    Deng, F.-G., Long, G.L.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69(5), 052319 (2004)CrossRefADSGoogle Scholar
  39. 39.
    Ting, G., Feng-Li, Y., Zhi-Xi, W.: A simultaneous quantum secure direct communication scheme between the central party and other m parties. Chin. Phys. Lett. 22(10), 2473 (2005)CrossRefADSGoogle Scholar
  40. 40.
    Wang, C., Deng, F.G., Long, G.L.: Multi-step quantum secure direct communication using multi-particle Green–Horne–Zeilinger state. Opt. Commun. 253(1), 15–20 (2005)CrossRefADSGoogle Scholar
  41. 41.
    Li, X.-H., Li, C.-Y., Deng, F.-G., Zhou, P., Liang, Y.-J., Zhou, H.-Y.: Quantum Secure Direct Communication with Quantum Encryption Based on Pure Entangled States. arXiv:quant-ph/0512014 (2005)
  42. 42.
    Jin, X.-R., Ji, X., Zhang, Y.-Q., Zhang, S., Hong, S.-K., Yeon, K.-H., Um, C.-I.: Three-party quantum secure direct communication based on GHZ states. Phys. Lett. A 354(1), 67–70 (2006)CrossRefADSGoogle Scholar
  43. 43.
    Zhong-Xiao, M., Yun-Jie, X.: Improvement of security of three-party quantum secure direct communication based on GHZ states. Chin. Phys. Lett. 24(1), 15 (2007)CrossRefADSGoogle Scholar
  44. 44.
    Wójcik, A.: Eavesdropping on the ping–pong quantum communication protocol. Phys. Rev. Lett. 90(15), 157901 (2003)CrossRefADSGoogle Scholar
  45. 45.
    Han, Y.-G., Yin, Z.-Q., Li, H.-W., Chen, W., Wang, S., Guo, G.-C., Han, Z.-F.: Security of modified ping–pong protocol in noisy and lossy channel. Sci. Rep. 4, 4936 (2014)CrossRefGoogle Scholar
  46. 46.
    Zawadzki, P.: Security of ping–pong protocol based on pairs of completely entangled qudits. Quantum Inf. Process. 11, 1–12 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  47. 47.
    Zawadzki, P.: The ping–pong protocol with a prior privacy amplification. Int. J. Quantum Inf. 10(03), 1250032 (2012)CrossRefzbMATHGoogle Scholar
  48. 48.
    Cai, Q.-Y., Li, B.-W.: Improving the capacity of the Boström–Felbinger protocol. Phys. Rev. A 69(5), 054301 (2004)CrossRefADSGoogle Scholar
  49. 49.
    Cai, Q.-Y., Li, B.-W.: Deterministic secure communication without using entanglement. Chin. Phys. Lett. 21, 601 (2004)CrossRefADSGoogle Scholar
  50. 50.
    Cai, Q.-Y.: Eavesdropping on the two-way quantum communication protocols with invisible photons. Phys. Lett. A 351, 23 (2006)CrossRefzbMATHADSGoogle Scholar
  51. 51.
    Zawadzki, P., Miszczak, J.A.: A general scheme for information interception in the ping-pong protocol. Adv. Math. Phys. 2016, 3162012 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  52. 52.
    Li, J., Song, D.J., Guo, X.J.: An improved security detection strategy based on w state in ping–pong protocol. Chin. J. Electron. 21, 117–120 (2012)Google Scholar
  53. 53.
    Zawadzki, P.: Improving security of the ping–pong protocol. Quantum Inf. Process. 12(1), 149–155 (2012)MathSciNetCrossRefzbMATHADSGoogle Scholar
  54. 54.
    Zhang, Z., Man, Z., Li, Y.: Improving wójcik’s eavesdropping attack on the ping–pong protocol. Phys. Lett. A 333(1), 46–50 (2004)MathSciNetCrossRefzbMATHADSGoogle Scholar
  55. 55.
    Eugene, V.V.: Non-coherent attack on the ping–pong protocol with completely entangled pairs of qutrits. Quantum Inf. Process. 10(2), 189–202 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  56. 56.
    Chamoli, A., Bhandari, C.M.: Secure direct communication based on ping–pong protocol. Quantum Inf. Process. 8(4), 347–356 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  57. 57.
    Boström, K., Felbinger, T.: On the security of the ping–pong protocol. Phys. Lett. A 372(22), 3953–3956 (2008)MathSciNetCrossRefzbMATHADSGoogle Scholar
  58. 58.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2010)CrossRefzbMATHGoogle Scholar
  59. 59.
    Boström, K., Felbinger, T.: On the security of the ping-pong protocol. Phys. Lett. A 372, 3953–3956 (2008)MathSciNetCrossRefzbMATHADSGoogle Scholar
  60. 60.
    Srikanth, R., Banerjee, S.: An environment-mediated quantum deleter. Phys. Lett. A 367(4), 295–299 (2007)MathSciNetCrossRefzbMATHADSGoogle Scholar
  61. 61.
    Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information. Quantum 546, 1231 (2000)zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.IIT JodhpurJodhpurIndia
  2. 2.Poornaprajna Institute of Scientific ResearchBangaloreIndia
  3. 3.Graduate StudiesManipal Academy of Higher EducationManipalIndia

Personalised recommendations