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Quantum cryptography over non-Markovian channels

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Abstract

A three-party scheme for secure quantum communication, namely controlled quantum dialogue (CQD), is analyzed under the influence of non-Markovian channels. By comparing with the corresponding Markovian cases, it is seen that the average fidelity can be maintained for relatively longer periods of time. Interestingly, a number of facets of quantum cryptography, such as quantum secure direct communication, deterministic secure quantum communication and their controlled counterparts, quantum dialogue, quantum key distribution, quantum key agreement, can be reduced from the CQD scheme. Therefore, the CQD scheme is analyzed under the influence of damping, dephasing and depolarizing non-Markovian channels, and subsequently, the effect of these non-Markovian channels on the other schemes of secure quantum communication is deduced from the results obtained for CQD. The damped non-Markovian channel causes a periodic revival in the fidelity, while fidelity is observed to be sustained under the influence of the dephasing non-Markovian channel.

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Notes

  1. Here, and in what follows, all the qubits traveling from one party to another are sent in a secure manner, i.e., to send a sequence of n travel qubits, an equal number of decoy qubits are inserted randomly in the original sequence of the travel qubits, and subsequently, these decoy qubits are measured to check the existence of eavesdropper(s). Various choices of decoy qubits and the corresponding principles of security are discussed in [63].

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Acknowledgements

AP and KT thank Defense Research & Development Organization (DRDO), India, for the support provided through the Project Number ERIP/ER/1403163/M/01/1603. SB acknowledges support by the Project Number 03(1369)/16/EMR-II funded by Council of Scientific and Industrial Research, New Delhi.

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Authors and Affiliations

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

    Kishore Thapliyal & Anirban Pathak

  2. Indian Institute of Technology Jodhpur, Jodhpur, Rajasthan, 342011, India

    Subhashish Banerjee

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  1. Kishore Thapliyal
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  2. Anirban Pathak
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  3. Subhashish Banerjee
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Correspondence to Anirban Pathak.

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Thapliyal, K., Pathak, A. & Banerjee, S. Quantum cryptography over non-Markovian channels. Quantum Inf Process 16, 115 (2017). https://doi.org/10.1007/s11128-017-1567-1

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