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Quantum cryptography over non-Markovian channels

A set of schemes for secure quantum communication are analyzed under the influence of non-Markovian channels. By comparing with the corresponding Markovian cases, it is seen that the average fidelity in all these schemes can be maintained for relatively longer periods of time. The effects of non-Markovian noise on 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, etc., have been extensively investigated. Specifically, a scheme for controlled quantum dialogue (CQD) is analyzed over 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. The depolarizing channel, as well as the other non-Markovian channels discussed here, show that the obtained average fidelity subjected to noisy environment depends on the strength of coupling between the quantum system with its surroundings and the number of rounds of quantum communication involved in a particular scheme.