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Kak’s three-stage protocol of secure quantum communication revisited: hitherto unknown strengths and weaknesses of the protocol

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Abstract

Kak’s three-stage protocol for quantum key distribution is revisited with special focus on its hitherto unknown strengths and weaknesses. It is shown that this protocol can be used for secure direct quantum communication. Further, the implementability of this protocol in the realistic situation is analyzed by considering various Markovian noise models. It is found that the Kak’s protocol and its variants in their original form can be implemented only in a restricted class of noisy channels, where the protocols can be transformed to corresponding protocols based on logical qubits in decoherence free subspace. Specifically, it is observed that Kak’s protocol can be implemented in the presence of collective rotation and collective dephasing noise, but cannot be implemented in its original form in the presence of other types of noise, like amplitude and phase damping noise. Further, the performance of the protocol in the noisy environment is quantified by computing average fidelity under various noise models, and subsequently a set of preferred states for secure communication in noisy environment have also been identified.

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Notes

  1. The term “unconditional security” is frequently used in the literature of QKD assuming the devices used to implement are ideal and trustworthy.

  2. Note that [24] contradicts the well-established results of Ref. [25] and the protocol reported [24] is not loophole free.

  3. An alternative definition exists in the literature [38] according to which Kak’s scheme should be viewed as a scheme for deterministic QKD since it does not involve block transmission. However, a deterministic QKD scheme can be adapted to perform direct secure quantum communication if the sender encrypts the message with a randomly chosen private key before sending it to the receiver using deterministic QKD and revealing the key only when she ensures the secure transmission of ciphertext.

  4. Here, it may be noted that although Kak’s protocol in its original form would not work under the CD noise, there are techniques to use logical qubits and thus to exploit the advantage of a decoherence free subspace to realize Kak’s protocol in presence of CD noise [54, 56], but no such decoherence free subspace is known for the AD and PD noise.

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Acknowledgements

KT thanks CSIR, India, for the support provided through Senior Research Fellowship. AP thanks Defense Research & Development Organization (DRDO), India, for the support provided through the Project Number ERIP/ER/ 1403163/M/01/1603.

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

    Kishore Thapliyal & Anirban Pathak

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  1. Kishore Thapliyal
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Thapliyal, K., Pathak, A. Kak’s three-stage protocol of secure quantum communication revisited: hitherto unknown strengths and weaknesses of the protocol. Quantum Inf Process 17, 229 (2018). https://doi.org/10.1007/s11128-018-2001-z

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