Quantum Collapse Bell Inequalities

TL;DR

This paper introduces Bell inequalities tailored for quantum systems that incorporate wave function collapse, enabling tests of hidden-variable theories through phase space violations linked to Wigner function negativity.

Contribution

It develops a new class of Bell inequalities that account for wave function collapse and applies them to phase space, broadening the scope of Bell tests beyond traditional setups.

Findings

Violations of the inequalities demonstrate non-classical phase space features.

The inequalities are applicable to any observable decomposable into non-commuting projectors.

Examples show both local and non-local violations related to Wigner function negativity.

Abstract

We propose Bell inequalities for discrete or continuous quantum systems which test the compatibility of quantum physics with an interpretation in terms of deterministic hidden-variable theories. The wave function collapse that occurs in a sequence of quantum measurements enters the upper bound via the concept of quantum conditional probabilities. The resulting hidden-variable inequality is applicable to an arbitrary observable that is decomposable into a weighted sum of non-commuting projectors. We present local and non-local examples of violation of generalized Bell inequalities in phase space, which sense the negativity of the Wigner function.