Reliable numerical key rates for quantum key distribution

Adam Winick, Norbert Lütkenhaus, and Patrick J. Coles

Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, N2L3G1 Waterloo, Ontario, Canada

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In this work, we present a reliable, efficient, and tight numerical method for calculating key rates for finite-dimensional quantum key distribution (QKD) protocols. We illustrate our approach by finding higher key rates than those previously reported in the literature for several interesting scenarios (e.g., the Trojan-horse attack and the phase-coherent BB84 protocol). Our method will ultimately improve our ability to automate key rate calculations and, hence, to develop a user-friendly software package that could be used widely by QKD researchers.

The main theoretical challenge in quantum key distribution (QKD) is to evaluate the performance of a given protocol, as quantified by the key rate (bits of secret key per transmitted quantum signal). Analytical methods for key rate calculations have made significant progress for specific
protocols, but often tend not to be robust to device imperfections or changes in protocol structure. Numerical methods naturally have more robustness, but new issues arise with numerics such as the reliability and efficiency (i.e., computation time) of the calculation. In this work, we present a reliable, efficient, and tight numerical method for calculating key rates for finite-dimensional QKD protocols. Due to its tightness, our method gives higher key rates than literature methods for several
technologically important scenarios, for example, for the Trojan-horse attack and for the phase-coherent BB84 protocol. Our method will ultimately allow researchers to automate key rate calculations and hence to develop user-friendly software for QKD security analysis.

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