Bell Non-Locality in Many Body Quantum Systems with Exponential Decay of Correlations

TL;DR

This paper investigates Bell non-locality in many-body quantum systems with exponential decay of correlations, showing that such systems behave almost locally and only weakly violate Bell inequalities, supported by theoretical proofs and examples.

Contribution

It demonstrates that many-body quantum systems with exponential decay of correlations exhibit near-local behavior, limiting Bell inequality violations, with comprehensive theoretical analysis and counter-examples.

Findings

Large family of systems behave almost locally

Bell inequality violations are minimal in these systems

Provides rigorous proofs and illustrative examples

Abstract

Using Bell-inequalities as a tool to explore non-classical physical behaviours, in this paper we analyze what one can expect to find in many-body quantum physics. Concretely, framing the usual correlation scenarios as a concrete spin-lattice, we want to know whether or not it is possible to violate a Bell-inequality restricted to this scenario. Using clustering theorems, we are able to show that a large family of quantum many-body systems behave almost locally, violating Bell-inequalities (if so) only by a non-significant amount. We also provide examples, explain some of our assumptions via counter-examples and present all the proofs for our theorems. We hope the paper is self-contained.