Secrecy extraction from no-signalling correlations

Abstract

Quantum cryptography shows that one can guarantee the secrecy of correlation on the sole basis of the laws of physics, that is without limiting the computational power of the eavesdropper. The usual security proofs suppose that the authorized partners, Alice and Bob, have a perfect knowledge and control of their quantum systems and devices; for instance, they must be sure that the logical bits have been encoded in true qubits, and not in higher-dimensional systems. In this paper, we present an approach that circumvents this strong assumption. We define protocols, both for the case of bits and for generic $d$-dimensional outcomes, in which the security is guaranteed by the very structure of the Alice-Bob correlations, under the no-signalling condition. The idea is that, if the correlations cannot be produced by shared randomness, then Eve has poor knowledge of Alice's and Bob's symbols. The present study assumes, on the one hand that the eavesdropper Eve performs only individual attacks (this is a limitation to be removed in further work), on the other hand that Eve can distribute any correlation compatible with the no-signalling condition (in this sense her power is greater than what quantum physics allows). Under these assumptions, we prove that the protocols defined here allow extracting secrecy from noisy correlations, when these correlations violate a Bell-type inequality by a sufficiently large amount. The region, in which secrecy extraction is possible, extends within the region of correlations achievable by measurements on entangled quantum states.

23 pages, 4 figures

References in corpus (2)

• Distillation of secret key and entanglement from quantum states
• Efficient quantum key distribution secure against no-signalling eavesdroppers

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• Device-independent security of quantum cryptography against collective attacks
• Device-independent quantum key distribution secure against collective attacks
• Testing the Hilbert space dimension
• Unbounded violation of tripartite Bell inequalities
• Recovering part of the quantum boundary from information causality
• Observation of tunable Popescu-Rohrlich correlations through post-selection of a gaussian state
• Experimental quantum key distribution based on a Bell test
• On the local and non-local content of bipartite qubit and qutrit correlations
• Entanglement Enhances Security in Secret Sharing
• Finite de Finetti theorem for conditional probability distributions describing physical theories