Quantum key distribution rates from semidefinite programming

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.

11+5 pages, 3 figures. Minor improvements, published version

References in corpus (4)

• Distillation of secret key and entanglement from quantum states
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Symmetry groups, semidefinite programs, and sums of squares
• Distribution of genuine high-dimensional entanglement over 10.2 km of noisy metropolitan atmosphere

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• Quantum key distribution rates from non-symmetric conic optimization
• Optimising the relative entropy under semidefinite constraints
• Numerical security analysis for quantum key distribution with partial state characterization
• Quantum Key Distribution with Imperfections: Recent Advances in Security Proofs
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• Revealing effects of local dimension on variable-range interacting model by connecting Lieb-Robinson bounds and multipartite entanglement