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

TL;DR

This paper revisits Kak's three-stage quantum communication protocol, revealing its potential for secure direct communication and analyzing its implementation limitations under various realistic noise conditions.

Contribution

It uncovers the protocol's strengths for secure direct communication and details its implementability constraints in noisy environments, especially in decoherence-free subspaces.

Findings

Kak's protocol can be used for secure direct quantum communication.

Implementation is feasible only in specific noisy channels like collective rotation and dephasing.

Average fidelity varies with noise models, identifying preferred states for secure communication.

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 damping 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.