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.

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]