Laboratoire d’Information Quantique, Université libre de Bruxelles (ULB), Belgium
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Abstract
According to the entropy accumulation theorem, proving the unconditional security of a device-independent quantum key distribution protocol reduces to deriving tradeoff functions, i.e., bounds on the single-round von Neumann entropy of the raw key as a function of Bell linear functionals, conditioned on an eavesdropper’s quantum side information. In this work, we describe how the conditional entropy can be bounded in the 2-input/2-output setting, where the analysis can be reduced to qubit systems, by combining entropy bounds for variants of the well-known BB84 protocol with quantum constraints on qubit operators on the bipartite system shared by Alice and Bob. The approach gives analytic bounds on the entropy, or semi-analytic ones in reasonable computation time, which are typically close to optimal. We illustrate the approach on a variant of the device-independent CHSH QKD protocol where both bases are used to generate the key as well as on a more refined analysis of the original single-basis variant with respect to losses. We obtain in particular a detection efficiency threshold slightly below 80.26%, within reach of current experimental capabilities.
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Cited by
[1] D. P. Nadlinger, P. Drmota, B. C. Nichol, G. Araneda, D. Main, R. Srinivas, D. M. Lucas, C. J. Ballance, K. Ivanov, E. Y. -Z. Tan, P. Sekatski, R. L. Urbanke, R. Renner, N. Sangouard, and J. -D. Bancal, “Experimental quantum key distribution certified by Bell’s theorem”, Nature 607 7920, 682 (2022).
[2] Lewis Wooltorton, Peter Brown, and Roger Colbeck, “Tight Analytic Bound on the Trade-Off between Device-Independent Randomness and Nonlocality”, Physical Review Letters 129 15, 150403 (2022).
[3] Víctor Zapatero, Tim van Leent, Rotem Arnon-Friedman, Wen-Zhao Liu, Qiang Zhang, Harald Weinfurter, and Marcos Curty, “Advances in device-independent quantum key distribution”, arXiv:2208.12842.
[4] Karol Łukanowski, Maria Balanzó-Juandó, Máté Farkas, Antonio Acín, and Jan Kołodyński, “Upper bounds on key rates in device-independent quantum key distribution based on convex-combination attacks”, arXiv:2206.06245.
[5] Federico Grasselli, Gláucia Murta, Hermann Kampermann, and Dagmar Bruß, “Boosting device-independent cryptography with tripartite nonlocality”, arXiv:2209.12828.
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