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Applications of quantum cryptographic switch: various tasks related to controlled quantum communication can be performed using Bell states and permutation of particles. (English) Zbl 1327.81171

Summary: Recently, several aspects of controlled quantum communication (e.g., bidirectional controlled state teleportation, controlled quantum secure direct communication, controlled quantum dialogue, etc.) have been studied using \(n\)-qubit \((n\geq 3)\) entanglement. Specially, a large number of schemes for bidirectional controlled state teleportation are proposed using \(m\)-qubit entanglement \((m\in\{5,6,7\})\). Here, we propose a set of protocols to illustrate that it is possible to realize all these tasks related to controlled quantum communication using only Bell states and permutation of particles. As the generation and maintenance of a Bell state is much easier than a multi-partite entanglement, the proposed strategy has a clear advantage over the existing proposals. Further, it is shown that all the schemes proposed here may be viewed as applications of the concept of quantum cryptographic switch which was recently introduced by some of us. The performances of the proposed protocols as subjected to the amplitude damping and phase damping noise on the channels are also discussed.

MSC:

81P94 Quantum cryptography (quantum-theoretic aspects)
94A60 Cryptography

References:

[1] Bennett, C.H., Brassard, G., Crï¿peau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895 (1993) · Zbl 1051.81505 · doi:10.1103/PhysRevLett.70.1895
[2] Karlsson, A., Bourennane, M.: Quantum teleportation using three-particle entanglement. Phys. Rev. A 58, 4394 (1998) · doi:10.1103/PhysRevA.58.4394
[3] Pathak, A., Banerjee, A.: Efficient quantum circuits for perfect and controlled teleportation of \[n\] n-qubit non-maximally entangled states of generalized Bell-type. Int. J. Quantum Inf. 9, 389 (2011) · Zbl 1216.81042 · doi:10.1142/S0219749911007368
[4] Hillery, M., Buzek, V., Bertaiume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999) · Zbl 1368.81066 · doi:10.1103/PhysRevA.59.1829
[5] Wang, X.W., Xia, L.-X., Wang, Z.-Y., Zhang, D.-Y.: Hierarchical quantum-information splitting. Opt. Commun. 283, 1196 (2010) · doi:10.1016/j.optcom.2009.11.015
[6] Shukla, C., Pathak, A.: Hierarchical quantum communication. Phys. Lett. A 377, 1337 (2013) · Zbl 1292.81019 · doi:10.1016/j.physleta.2013.04.010
[7] Pati, A.K.: Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A 63, 014302 (2000) · doi:10.1103/PhysRevA.63.014302
[8] Huelga, S.F., Vaccaro, J.A., Chefles, A., Plenio, M.B.: Quantum remote control: teleportation of unitary operations. Phys. Rev. A 63, 042303 (2001) · Zbl 1255.81109 · doi:10.1103/PhysRevA.63.042303
[9] Huelga, S.F., Plenio, M.B., Vaccaro, J.A.: Remote control of restricted sets of operations: teleportation of angles. Phys. Rev. A 65, 042316 (2002) · doi:10.1103/PhysRevA.65.042316
[10] Zha, X.-W., Zou, Z.-C., Qi, J.-X., Song, H.-Y.: Bidirectional quantum controlled teleportation via five-qubit cluster state. Int. J. Theor. Phys. 52, 1740 (2013) · doi:10.1007/s10773-012-1208-5
[11] Zha, X.-W., Song, H.-Y., Ma, G.-L.: Bidirectional swapping quantum controlled teleportation based on maximally entangled five-qubit state. quant-ph/1006.0052 (2010)
[12] Li, Y.-H., Nie, L-p: Bidirectional controlled teleportation by using a five-qubit composite GHZ-Bell state. Int. J. Theor. Phys. 52, 1630 (2013) · doi:10.1007/s10773-013-1484-8
[13] Shukla, C., Banerjee, A., Pathak, A.: Bidirectional controlled teleportation by using 5-qubit states: a generalized view. Int. J. Theor. Phys. 52, 3790 (2013) · doi:10.1007/s10773-013-1684-2
[14] Li, Y.-H., Li, X.-L., Sang, M.-H., Nie, Y.-Y., Wang, Z.-S.: Bidirectional controlled quantum teleportation and secure direct communication using five-qubit entangled state. Quantum Inf. Process. 12, 3835 (2013) · Zbl 1303.81061 · doi:10.1007/s11128-013-0638-1
[15] Duan, Y.-J., Zha, X.-W.: Bidirectional quantum controlled teleportation via a six-qubit entangled state. Int. J. Theor. Phys. 53, 3780 (2014) · Zbl 1307.81022 · doi:10.1007/s10773-014-2131-8
[16] Fu, H.-Z., Tian, X.-L., Hu, Y.: A general method of selecting quantum channel for bidirectional quantum teleportation. Int. J. Theor. Phys. 53, 1840 (2014) · Zbl 1298.81035 · doi:10.1007/s10773-013-1985-5
[17] Chen, Y.: Bidirectional quantum controlled teleportation by using a genuine six-qubit entangled state. Int. J. Theor. Phys. 54, 269 (2014) · Zbl 1304.81050
[18] An, Y.: Bidirectional controlled teleportation via six-qubit cluster state. Int. J. Theor. Phys. 52, 3870 (2013) · Zbl 1282.81044 · doi:10.1007/s10773-013-1694-0
[19] Duan, Y.-J., Zha, X.-W., Sun, X.-M., Xia, J.-F.: Bidirectional quantum controlled teleportation via a maximally seven-qubit entangled state. Int. J. Theor. Phys. 53, 2697 (2014) · Zbl 1308.81045 · doi:10.1007/s10773-014-2065-1
[20] Dong, Li, Xiu, X.-M., Gao, Y.-J., Chi, F.: A controlled quantum dialogue protocol in the network using entanglement swapping. Opt. Commun. 281, 6135 (2008) · doi:10.1016/j.optcom.2008.09.030
[21] Xia, Y., Fu, C.-B., Zhang, S., Hong, S.-K., Yeon, K.-H., Um, C.-I.: Quantum dialogue by using the GHZ state. J. Korean Phys. Soc. 48, 24 (2006)
[22] Hassanpour, S., Houshmand, M.: Efficient controlled quantum secure direct communication based on GHZ-like states. Quantum Inf. Process 14, 739 (2014) · Zbl 1311.81094
[23] Srinatha, N., Omkar, S., Srikanth, R., Banerjee, S., Pathak, A.: The quantum cryptographic switch. Quantum Inf. Process. 13, 59 (2014) · doi:10.1007/s11128-012-0487-3
[24] Deng, F.-G., Long, G.L.: Controlled order rearrangement encryption for quantum key distribution. Phys. Rev. A 68, 042315 (2003) · doi:10.1103/PhysRevA.68.042315
[25] 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) · Zbl 1317.81086 · doi:10.1142/S0219749912410092
[26] Shukla, C., Banerjee, A., Pathak, A.: Improved protocols of secure quantum communication using W states. Int. J. Theor. Phys. 52, 1914 (2013) · doi:10.1007/s10773-012-1311-7
[27] Banerjee, A., Pathak, A.: Maximally efficient protocols for direct secure quantum communication. Phys. Lett. A 376, 2944 (2012) · doi:10.1016/j.physleta.2012.08.032
[28] Yadav, P., Srikanth, R., Pathak, A.: Two-step orthogonal-state-based protocol of quantum secure direct communication with the help of order-rearrangement technique. Quantum Inf. Process. 13, 2731 (2014) · Zbl 1304.81067 · doi:10.1007/s11128-014-0825-8
[29] An, N.B.: Quantum dialogue. Phys. Lett. A 328, 6-10 (2004) · Zbl 1134.81338 · doi:10.1016/j.physleta.2004.06.009
[30] 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 (2013) · Zbl 1428.81048 · doi:10.1016/j.physleta.2012.12.024
[31] Bennett, C. H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings of the IEEE international conference on computers, systems, and signal processing, Bangalore, India, p. 175 (1984) · Zbl 1306.81030
[32] Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991) · Zbl 0990.94509 · doi:10.1103/PhysRevLett.67.661
[33] Boström, K., Felbinger, T.: Deterministic secure direct communication using entanglement. Phys. Rev. Lett. 89, 187902 (2002) · doi:10.1103/PhysRevLett.89.187902
[34] Cai, Q.-Y., Li, B-w: Improving the capacity of the Boström-Felbinger protocol. Phys. Rev. A 69, 054301 (2004) · doi:10.1103/PhysRevA.69.054301
[35] 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) · doi:10.1103/PhysRevA.68.042317
[36] Pathak, A.: Elements of Quantum Computation and Quantum Communication. CRC Press, Boca Raton (2013) · Zbl 1280.81002
[37] Shukla, C., Alam, N., Pathak, A.: Protocols of quantum key agreement solely using Bell states and Bell measurement. Quantum Inf. Process. 13, 2391 (2014) · Zbl 1305.81068 · doi:10.1007/s11128-014-0784-0
[38] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, New Delhi (2008) · Zbl 1049.81015
[39] Guan, X.-W., Chen, X.-B., Wang, L.-C., Yang, Y.-X.: Joint remote preparation of an arbitrary two-qubit state in noisy environments. Int. J. Theor. Phys. 53, 2236 (2014) · Zbl 1298.81036 · doi:10.1007/s10773-014-2024-x
[40] Sharma, V., Shukla, C., Banerjee, S., & Pathak, A.: Controlled bidirectional remote state preparation in noisy environment: a generalized view. arXiv:1409.0833 (2014) · Zbl 1325.81039
[41] Srikanth, R., Banerjee, S.: Squeezed generalized amplitude damping channel. Phys. Rev. A 77, 012318 (2008) · doi:10.1103/PhysRevA.77.012318
[42] Macchiavello, C., Palma, G.M.: Entanglement-enhanced information transmission over a quantum channel with correlated noise. Phys. Rev. A 65, 050301 (2002) · doi:10.1103/PhysRevA.65.050301
[43] Cao, T.B., An, N.B.: Deterministic controlled bidirectional remote state preparation. Adv. Nat. Sci. Nanosci. Nanotechnol. 5, 015003 (2014) · doi:10.1088/2043-6262/5/1/015003
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