Simple and practical DIQKD security analysis via BB84-type uncertainty relations and Pauli correlation constraints

• URL: http://arxiv.org/abs/2107.08894v3
• Date: Tue, 18 Oct 2022 08:43:25 GMT
• Title: Simple and practical DIQKD security analysis via BB84-type uncertainty relations and Pauli correlation constraints
• Authors: Michele Masini, Stefano Pironio, Erik Woodhead
• Abstract summary: In this work, we describe how the conditional entropy can be bounded in the 2-input/2-output setting. We illustrate the approach on a variant of the device-independent CHSH QKD protocol where both bases are used to generate the key.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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