Information-based measure of nonlocality

Abstract

Quantum nonlocality concerns correlations among spatially separated systems that cannot be classically explained without post-measurement communication among the parties. Thus, a natural measure of nonlocal correlations is provided by the minimal amount of communication required for classically simulating them. In this paper, we present a method to compute the minimal communication cost, which we call nonlocal capacity, for any general nonsignaling correlations. This measure turns out to have an important role in communication complexity and can be used to discriminate between local and nonlocal correlations, as an alternative to the violation of Bell's inequalities.

Substantial improvements have been made to the readablity of the paper. In particular, we provide a detailed justification of the adopted measure of communication. The order of Theorem 1 and 2 has been swapped and we have first considered the case of single-shot simulations, which gives a clearer clue of the ideas used for the case of parallel simulations. An appendix added

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• Quantifying Bell non-locality with the trace distance
• Leggett-Garg Macrorealism and temporal correlations
• Non-Locality of Experimental Qutrit Pairs
• Memory cost of temporal correlations
• Ticking-clock performance enhanced by nonclassical temporal correlations
• Optimal measurements for nonlocal correlations
• Reality, Causality, and Quantum Theory
• Quantum correlation generation capability of experimental processes