Extremal Quantum Correlations and Cryptographic Security

Abstract

We investigate a fundamental property of device independent security in quantum cryptography by characterizing probability distributions which are necessarily independent of the measurement results of any eavesdropper. We show that probability distributions that are secure in this sense are exactly the extremal quantum probability distributions. This allows us to give a characterization of security in algebraic terms. We apply the method to common examples for two-party as well as multi-party setups and present a scheme for verifying security of probability distributions with two parties, two measurement settings, and two outcomes.

7 pages, 2 figures, revised version, accepted for publication in Phys. Rev. Lett

References in corpus (5)

• Device-independent security of quantum cryptography against collective attacks
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Non-local correlations as an information theoretic resource
• Secure device-independent quantum key distribution with causally independent measurement devices
• The noncommutative Choquet boundary

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• Device-independent secure correlations in sequential quantum scenarios