Monogamy of nonlocal quantum correlations

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.Comment: This is the submitted version. The refereed version, which contains an additional result about strong parallel repetition and corrects some typos, is available on my personal web site at http://bentoner.com/papers/monogamyrs.pdf [PDF