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Monogamy of nonlocal quantum correlations

Ben Toner
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Abstract

We describe a new technique for obtaining Tsirelson bounds, or upper bounds on the quantum value of a Bell inequality. Since quantum correlations do not allow signaling, we obtain a Tsirelson bound by maximizing over all no-signaling probability distributions. This maximization can be cast as a linear program. In a setting where three parties, A, B, and C, share an entangled quantum state of arbitrary dimension, we: (i) bound the trade-off between AB's and AC's violation of the CHSH inequality, and (ii) demonstrate that forcing B and C to be classically correlated prevents A and B from violating certain Bell inequalities, relevant for interactive proof systems and cryptography.

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Ben Toner. 2009-01-17. Monogamy of nonlocal quantum correlations. https://doi.org/10.1098/rspa.2008.0149

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