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arXiv:2212.13089 · The European Physical Journal D

New protocols for quantum key distribution with explicit upper and lower bound on secret key rate

Arindam Dutta, Anirban Pathak

Published May 1, 2025• 1 citation
arXivHTMLPDF
DOI
10.1140/epjd/s10053-025-01000-2

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We present a simple method to obtain an upper bound on the achievable secret key rate in quantum key distribution (QKD) protocols that use only unidirectional classical communication during the public-discussion phase. This method is based on a necessary precondition for one-way secret key distillation; the legitimate users need to prove that there exists no quantum state having a symmetric extension that is compatible with the available measurements results. The main advantage of the obtained upper bound is that it can be formulated as a semidefinite program, which can be efficiently solved. We illustrate our results by analyzing two well-known qubit-based QKD protocols: the four-state protocol and the six-state protocol.
This paper aims to present a mathematical tool useful for quantum key distribution network configuration. In particular, the paper studies the throughput of secret key distribution in a quantum key distribution network with trusted repeaters. In addition, the backlog of secret keys at a trusted repeater is also investigated. The analysis is based on the queueing principle of secret keys in the trusted repeater, implied by that the transmission of secret keys in the network is store-and-forward. The obtained results are applied to a discrete-variable protocol with weak coherent pulse sources, where realistic system parameters are integrated in the analysis. It is shown that, if the secret key rates on the transmission path are different, the transient throughput of secret key distribution through the network also vary, located between an upper bound and a lower bound of the secrete key distribution rate.