Complementary contributions of indeterminism and signalling to quantum correlations

Abstract

Simple quantitative measures of indeterminism and signalling, $I$ and $S$, are defined for models of statistical correlations. It is shown that any such model satisfies a generalised Bell-type inequality, with tight upper bound B(I,S). This upper bound explicitly quantifies the complementary contributions required from indeterminism and signalling, for modelling any given violation of the standard Bell-CHSH inequality. For example, all models of the maximum quantum violation must either assign no more than 80% probability of occurrence to some underlying event, and/or allow a nonlocal change of at least 60% in an underlying marginal probability of one observer in response to a change in measurement setting by a distant observer. The results yield a corresponding complementarity relation between the numbers of local random bits and nonlocal signalling bits required to model a given violation. A stronger relation is conjectured for simulations of singlet states. Signalling appears to be a useful resource only if a `gap' condition is satisfied, corresponding to being able to nonlocally flip some underlying marginal probability $p$ to its complementary value 1-p.

5.1 pages, restructured with expanded information-theoretic discussion and links to communication models, several refs added, to appear in PRA

References in corpus (6)

• Bell's theorem for general N-qubit states
• The Communication Cost of Simulating Bell Correlations
• Testing quantum correlations versus single-particle properties within Leggett's model and beyond
• Bell inequalities for continuous-variable correlations
• Nonlocal setting and outcome information for violation of Bell's inequality
• Optimal classical-communication-assisted local model of n-qubit Greenberger-Horne-Zeilinger correlations

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• Operational nonlocality