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.

arXiv comment11+5 pages, 3 figures. Minor improvements, published version

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• Resource-efficient high-dimensional entanglement detection via symmetric projections
• High-dimensional coherent one-way quantum key distribution
• High-dimensional quantum key distribution using a multi-plane light converter
• Continuous-variable quantum communication
• Security of differential phase shift QKD from relativistic principles
• The future of secure communications: device independence in quantum key distribution
• Comparison of confidence regions for quantum state tomography
• Harnessing high-dimensional temporal entanglement using limited interferometric setups
• 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
• Revealing effects of local dimension on variable-range interacting model by connecting Lieb-Robinson bounds and multipartite entanglement
• Composable Finite-Size Security of High-Dimensional Quantum Key Distribution Protocols