Bounding the set of quantum correlations

Abstract

We introduce a hierarchy of conditions necessarily satisfied by any distribution P(ab) representing the probabilities for two separate observers to obtain outcomes a and b when making local measurements on a shared quantum state. Each condition in this hierarchy is formulated as a semidefinite program. Our approach can be used to obtain upper-bounds on the quantum violation of an arbitrary Bell inequality. It yields, for instance, tight bounds for the violations of the Collins et al. inequalities.

5 pages, no figures. v2: minor modifications

References in corpus (1)

• Efficient quantum key distribution secure against no-signalling eavesdroppers

Cited by in corpus (16)

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• Bounds on Quantum Correlations in Bell Inequality Experiments
• Efficiency of higher dimensional Hilbert spaces for the violation of Bell inequalities
• Tsirelson's Problem
• Generalized Clauser-Horne-Shimony-Holt inequalities maximally violated by higher dimensional systems
• Locality, detection efficiencies, and probability polytopes
• Cryptography in a Quantum World
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