Quantum key distribution rates from semidefinite programming

• URL: http://arxiv.org/abs/2211.05725v2
• Date: Mon, 22 May 2023 14:15:25 GMT
• Title: Quantum key distribution rates from semidefinite programming
• Authors: Mateus Ara\'ujo, Marcus Huber, Miguel Navascu\'es, Matej Pivoluska, Armin Tavakoli
• Abstract summary: We introduce an efficient algorithm for computing the key rate in quantum key distribution protocols. The resulting algorithm is easy to implement and easy to use. We use it to reanalyse experimental data to demonstrate how higher key rates can be achieved.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Computing the key rate in quantum key distribution (QKD) protocols is a long standing challenge. Analytical methods are limited to a handful of protocols with highly symmetric measurement bases. Numerical methods can handle arbitrary measurement bases, but either use the min-entropy, which gives a loose lower bound to the von Neumann entropy, or rely on cumbersome dedicated algorithms. Based on a recently discovered semidefinite programming (SDP) hierarchy converging to the conditional von Neumann entropy, used for computing the asymptotic key rates in the device independent case, we introduce an SDP hierarchy that converges to the asymptotic secret key rate in the case of characterised devices. The resulting algorithm is efficient, easy to implement and easy to use. We illustrate its performance by recovering known bounds on the key rate and extending high-dimensional QKD protocols to previously intractable cases. We also use it to reanalyse experimental data to demonstrate how higher key rates can be achieved when the full statistics are taken into account.

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