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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

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Abstract

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 \((n\ge 3)\) 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.

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Notes

  1. By the same logic, we mean that unless Charlie measures his qubits and discloses the results, Alice and Bob do not know which Bell states they share.

  2. We can assume that Charlie has a quantum random number generator, and he has generated a large sequence of 0 and 1 through it. He uses the outcomes of the random number generator to decide which Bell state is to be prepared. For example, we may consider that if the first two bit values obtained from the random number generator are 00, 01, 10 and 11 then he prepares \(|\psi ^{+}\rangle ,|\psi ^{-}\rangle ,|\phi ^{+}\rangle ,\) and \(|\phi ^{-}\rangle ,\) respectively.

  3. BB84 subroutine [36] means eavesdropping is checked by following a procedure similar to that adopted in the original BB84 protocol. Specifically, BB84 subroutine implies that Alice (Bob) randomly selects half of the qubits received by her (him) to form a verification string. She (He) measures the verification qubits randomly in \(\left\{ |0\rangle ,|1\rangle \right\} \) or \(\left\{ |+\rangle ,|-\rangle \right\} \) basis and announces the measurement outcome, the position of that qubit in the string and the basis used for the particular measurement. Bob (Alice) also measures the corresponding qubit using the same basis (if needed) and compares his (her) result with the announced result of Alice (Bob) to detect eavesdropping.

  4. Usually fidelity \(F(\sigma ,\rho )\) of two quantum states \(\rho \) and \(\sigma \) is defined as \(F(\sigma ,\rho )=Tr\sqrt{\sigma ^{\frac{1}{2}}\rho \sigma ^{\frac{1}{2}}}.\) However, in the present work, we have used (6) as the definition of fidelity.

  5. AD and GAD channels are the special cases of SGAD channel.

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)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  2. Karlsson, A., Bourennane, M.: Quantum teleportation using three-particle entanglement. Phys. Rev. A 58, 4394 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  3. Pathak, A., Banerjee, A.: Efficient quantum circuits for perfect and controlled teleportation of \(n\)-qubit non-maximally entangled states of generalized Bell-type. Int. J. Quantum Inf. 9, 389 (2011)

    Article  MATH  Google Scholar 

  4. Hillery, M., Buzek, V., Bertaiume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  5. Wang, X.W., Xia, L.-X., Wang, Z.-Y., Zhang, D.-Y.: Hierarchical quantum-information splitting. Opt. Commun. 283, 1196 (2010)

    Article  ADS  Google Scholar 

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

    Article  MATH  MathSciNet  ADS  Google Scholar 

  7. Pati, A.K.: Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A 63, 014302 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  15. Duan, Y.-J., Zha, X.-W.: Bidirectional quantum controlled teleportation via a six-qubit entangled state. Int. J. Theor. Phys. 53, 3780 (2014)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  17. Chen, Y.: Bidirectional quantum controlled teleportation by using a genuine six-qubit entangled state. Int. J. Theor. Phys. 54, 269 (2014)

  18. An, Y.: Bidirectional controlled teleportation via six-qubit cluster state. Int. J. Theor. Phys. 52, 3870 (2013)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Google Scholar 

  22. Hassanpour, S., Houshmand, M.: Efficient controlled quantum secure direct communication based on GHZ-like states. Quantum Inf. Process 14, 739 (2014)

  23. Srinatha, N., Omkar, S., Srikanth, R., Banerjee, S., Pathak, A.: The quantum cryptographic switch. Quantum Inf. Process. 13, 59 (2014)

    Article  ADS  Google Scholar 

  24. Deng, F.-G., Long, G.L.: Controlled order rearrangement encryption for quantum key distribution. Phys. Rev. A 68, 042315 (2003)

    Article  ADS  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  26. Shukla, C., Banerjee, A., Pathak, A.: Improved protocols of secure quantum communication using W states. Int. J. Theor. Phys. 52, 1914 (2013)

    Article  MathSciNet  Google Scholar 

  27. Banerjee, A., Pathak, A.: Maximally efficient protocols for direct secure quantum communication. Phys. Lett. A 376, 2944 (2012)

    Article  ADS  Google Scholar 

  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)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  29. An, N.B.: Quantum dialogue. Phys. Lett. A 328, 6–10 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  ADS  Google Scholar 

  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)

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

    Article  MATH  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  36. Pathak, A.: Elements of Quantum Computation and Quantum Communication. CRC Press, Boca Raton (2013)

    MATH  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  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)

    Article  MATH  Google Scholar 

  40. Sharma, V., Shukla, C., Banerjee, S., & Pathak, A.: Controlled bidirectional remote state preparation in noisy environment: a generalized view. arXiv:1409.0833 (2014)

  41. Srikanth, R., Banerjee, S.: Squeezed generalized amplitude damping channel. Phys. Rev. A 77, 012318 (2008)

    Article  ADS  Google Scholar 

  42. Macchiavello, C., Palma, G.M.: Entanglement-enhanced information transmission over a quantum channel with correlated noise. Phys. Rev. A 65, 050301 (2002)

    Article  ADS  Google Scholar 

  43. Cao, T.B., An, N.B.: Deterministic controlled bidirectional remote state preparation. Adv. Nat. Sci. Nanosci. Nanotechnol. 5, 015003 (2014)

    Article  ADS  Google Scholar 

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Acknowledgments

AP and KT thank Department of Science and Technology (DST), India for support provided through the DST Project No. SR/S2/LOP-0012/2010.

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  1. Jaypee Institute of Information Technology, A-10, Sector-62, Noida, 201307, UP, India

    Kishore Thapliyal & Anirban Pathak

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  1. Kishore Thapliyal
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Correspondence to Anirban Pathak.

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Thapliyal, K., Pathak, A. Applications of quantum cryptographic switch: various tasks related to controlled quantum communication can be performed using Bell states and permutation of particles. Quantum Inf Process 14, 2599–2616 (2015). https://doi.org/10.1007/s11128-015-0987-z

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