Publication details

Quantum key distribution rates from semidefinite programming

Authors

ARAUJO Mateus HUBER Marcus NAVASCUES Miguel PIVOLUSKA Matej TAVAKOLI Armin

Year of publication 2023
Type Article in Periodical
Magazine / Source QUANTUM
MU Faculty or unit

Institute of Computer Science

Citation
Web https://quantum-journal.org/papers/q-2023-05-24-1019/
Doi http://dx.doi.org/10.1038/s41598-022-09881-8
Keywords quantum key distribution; semi-definite programming
Description 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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