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Quantum Information Processing

Erschienen in:

01.11.2014

Protocols of quantum key agreement solely using Bell states and Bell measurement

verfasst von: Chitra Shukla, Nasir Alam, Anirban Pathak

Erschienen in: Quantum Information Processing | Ausgabe 11/2014

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Abstract

Two protocols of quantum key agreement (QKA) that solely use Bell state and Bell measurement are proposed. The first protocol of QKA proposed here is designed for two-party QKA, whereas the second protocol is designed for multi-party QKA. The proposed protocols are also generalized to implement QKA using a set of multi-partite entangled states (e.g., 4-qubit cluster state and \(\Omega \) state). Security of these protocols arises from the monogamy of entanglement. This is in contrast to the existing protocols of QKA where security arises from the use of non-orthogonal state (non-commutativity principle). Further, it is shown that all the quantum systems that are useful for implementation of quantum dialogue and most of the protocols of secure direct quantum communication can be modified to implement protocols of QKA.

Vorheriger Artikel Multi-party quantum private comparison protocol with -level entangled states

Nächster Artikel Reexamining the security of fair quantum blind signature schemes

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Here subscripts A, B, C denote Alice, Bob, and Charlie, respectively.

In the stabilizer formalism of quantum error correction Pauli group is frequently used (see Section 10.5.1 of [32]). It is usually defined as \(G_{1}=\left\{ \pm I,\pm iI,\pm \sigma _{x},\pm i\sigma _{x},\pm \sigma _{y},\pm i\sigma _{y},\pm \sigma _{z},\pm i\sigma _{z}\right\} ,\) where \(\sigma _{i}\) is a Pauli matrix. The inclusion of \(\pm 1\) and \(\pm i\) ensures that \(G_{1}\) is closed under standard matrix multiplication, but the effect of \(\sigma _{i},\,-\sigma _{i},\, i\sigma _{i}\), and \(-i\sigma _{i}\) on a quantum state is the same. So in [33], we redefined the multiplication operation for two elements of the group in such a way that global phase is ignored from the product of matrices. This is consistent with the quantum mechanics and it gives us a modified Pauli group \(G_{1}=\{I,\,\sigma _{x},\, i\sigma _{y},\,\sigma _{z}\}=\{I,\, X,\, iY,\, Z\}.\)

In \(\mathrm{PP^{GV}}\)Alice does not need to disclose her key \(K_{A}\). Everything else is the same and as a consequence \(b=2n,\, q=4n\) and \(c=n\) with \(c\) being the number of bits in the message or key that is transmitted.

Bennett, C.H., Brassed, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, India, pp. 175–179 (1984)

Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–663 (1991)MathSciNetCrossRefADSMATH

Bennett, C.H.: Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68, 3121–3124 (1992)MathSciNetCrossRefADSMATH

Goldenberg, L., Vaidman, L.: Quantum cryptography based on orthogonal states. Phys. Rev. Lett. 75, 1239–1243 (1995)MathSciNetCrossRefADSMATH

Boström, K., Felbinger, T.: Deterministic secure direct communication using entanglement. Phys. Rev. Lett. 89, 187902 (2002)CrossRefADS

Lucamarini, M., Mancini, S.: Secure deterministic communication without entanglement. Phys. Rev. Lett. 94, 140501 (2005)CrossRefADS

Shukla, C., Pathak, A.: Hierarchical quantum communication. Phys. Lett. A 377, 1337–1344 (2013)MathSciNetCrossRefADSMATH

Zhou, N., Zeng, G., Xiong, J.: Quantum key agreement protocol. Electron. Lett. 40, 1149–1150 (2004)CrossRef

Chong, S.-K., Hwang, T.: Quantum key agreement protocol based on BB84. Optic Commun. 283, 1192–1195 (2010)CrossRefADS

10.

Yin, X.-R., Ma, W.-P., Liu, W.-Y.: Three-party quantum key agreement with two-photon entanglement. Int. J. Theor. Phys. 52, 3915–3921 (2013)MathSciNetCrossRefMATH

11.

Gisin, N., Renner, R., Wolf, S.: classical and quantum key agreement: Is there a classical analog to bound entanglement? Algorithmica 34, 389–412 (2002)MathSciNetCrossRefMATH

12.

Dijk, M. v., Koppelaar, A.: Quantum key agreement. In: Proceedings of IEEE International Symposium on Information Theory, IEEE, pp. 350–350 (1998)

13.

Tsai, C.W., Hwang, T.: On “Quantum key agreement protocol”, Technical Report, C-S-I-E, NCKU. Taiwan, R.O.C. (2009)

14.

Tsai, C.W., Chong S.K., Hwang, T.: Comment on quantum key agreement protocol with maximally entangled states. In: Proceedings of the 20th Cryptology and Information Security Conference (CISC 2010), pp. 210–213. National Chiao Tung University, Hsinchu, Taiwan, 27–28 May (2010)

15.

Chong, S.-K., Tsai, C.W., Hwang, T.: Improvement on “Quantum key agreement protocol with maximally entangled states”. Int. J. Theor. Phys. 50, 1793–1802 (2011)MathSciNetCrossRefMATH

16.

Liu, B., Gao, F., Huang, W., Wen, Q.-Y.: Multiparty quantum key agreement with single particles. Quantum Info. Process. 12, 1797–1805 (2013)MathSciNetCrossRefADSMATH

17.

Sun, Z., Zhang, C., Wang, B., Li, Q., Long, D.: Improvement on “multiparty quantum key agreement with single particles”. Quantum Inf. Process. 12, 3411–3420 (2013)MathSciNetCrossRefADSMATH

18.

Shi, R.-H., Zhong, H.: Multi-party quantum key agreement with Bell states and Bell measurements. Quantum Inf. Process. 12, 921–932 (2013)MathSciNetCrossRefADSMATH

19.

Huang, W., Wen, Q.-Y., Liu, B., Su Q., Gao, F.: Cryptanalysis of a multi-party quantum key agreement protocol with single particles, arXiv:1308.2777 (quant-ph)

20.

Diffie, W., Hellman, M.: New directions in cryptography. IEEE Trans. Inf. Theory 22, 644–654 (1976)MathSciNetCrossRefMATH

21.

Simon, B.-W., Menezes, A.: Authenticated Diffe-Hellman key agreement protocols in selected areas in cryptography. Springer, Berlin Heidelberg (1999)

22.

Victor, S.: Lower bounds for discrete logarithms and related problems. In Advances in Cryptology-EUROCRYPT’97, pp. 256–266. Springer, Berlin Heidelberg (1997)

23.

Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997)MathSciNetCrossRefMATH

24.

Hsueh, C.C., Chen, C.Y.: Quantum key agreement protocol with maximally entangled states. In: Proceedings of the 14th Information Security Conference, National Taiwan University of Science and Technology, Taipei, pp. 236–242 (2004)

25.

Noh, T.-G.: Counterfactual quantum cryptography. Phys. Rev. Lett. 103, 230501 (2009)MathSciNetCrossRefADS

26.

Shukla, C., Pathak, A., Srikanth, R.: Beyond the Goldenberg-Vaidman protocol: secure and efficient quantum communication using arbitrary, orthogonal, multi-particle quantum states. Int. J. Quantum Inf. 10, 1241009 (2012)MathSciNetCrossRef

27.

Yadav, P.,Srikanth R., Pathak, A.: Generalization of the Goldenberg-Vaidman QKD protocol, arXiv:1209.4304 (quant-ph)

28.

Avella, A., Brida, G., Degiovanni, I.P., Genovese, M., Gramegna, M., Traina, P.: Experimental quantum-cryptography scheme based on orthogonal states. Phys. Rev. A 82, 062309 (2010)CrossRefADS

29.

Ren, M., Wu, G., Wu, E., Zeng, H.: Experimental demonstration of counterfactual quantum key distribution. Laser Phys. 21, 755–760 (2011)CrossRefADS

30.

Brida, G., Cavanna, A., Degiovanni, I.P., Genovese, M., Traina, P.: Experimental realization of counterfactual quantum cryptography. Laser Phys. Lett. 9, 247–252 (2012)CrossRefADS

31.

Liu, Yang, et al.: Experimental demonstration of counterfactual quantum communication. Phys. Rev. Lett. 109, 030501 (2012)CrossRefADS

32.

Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, New Delhi (2008)

33.

Shukla, C., Kothari, V., Banerjee, A., Pathak, A.: On the group-theoretic structure of a class of quantum dialogue protocols. Phys. Lett. A 377, 518–527 (2013)MathSciNetCrossRefADS

34.

Deng, F.-G., Long, G.L., Liu, X.-S.: Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block. Phys. Rev. A 68, 042317 (2003)CrossRefADS

35.

Cai, Q.-Y., Li, B.-W.: Improving the capacity of the Boström-Felbinger protocol. Phys. Rev. A 69, 054301 (2004)CrossRefADS

36.

Pathak, A.: Elements of quantum computation and quantum communication. CRC Press, Boca Raton, USA (2013)MATH

37.

An, N.B.: Quantum dialogue. Phys. Lett. A 328, 6 (2004)MathSciNetCrossRefMATH

38.

Cabello, A.: Quantum key distribution in the Holevo limit. Phys. Rev. Lett. 85, 5635–5638 (2000)CrossRefADS

Titel: Protocols of quantum key agreement solely using Bell states and Bell measurement
verfasst von: Chitra Shukla
Nasir Alam
Anirban Pathak
Publikationsdatum: 01.11.2014
Verlag: Springer US
Erschienen in: Quantum Information Processing / Ausgabe 11/2014
Print ISSN: 1570-0755
Elektronische ISSN: 1573-1332
DOI: https://doi.org/10.1007/s11128-014-0784-0

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