Bell operator and Gaussian squeezed states in noncommutative quantum mechanics

TL;DR

This paper investigates whether noncommutative quantum mechanics introduces observable corrections to Bell inequalities using Gaussian squeezed states, concluding that noncommutativity does not affect Bell correlations in these states.

Contribution

It demonstrates that noncommutative quantum mechanics does not alter Bell operator measurements for Gaussian squeezed states, despite differences in covariance matrices.

Findings

No noticeable noncommutative corrections to Bell operator.

Squeezed states remain non-local in noncommutative quantum mechanics.

Covariance matrix evolution differs but does not affect Bell correlations.

Abstract

One examines putative corrections to the Bell operator due to the noncommutativity in the phase-space. Starting from a Gaussian squeezed envelop whose time evolution is driven by commutative (standard quantum mechanics) and noncommutative dynamics respectively, one concludes that, although the time evolving covariance matrix in the noncommutative case is different from the standard case, the squeezing parameter dominates and there are no noticeable noncommutative corrections to the Bell operator. This indicates that, at least for squeezed states, the privileged states to test Bell correlations, noncommutativity versions of quantum mechnics remains as non-local as quantum mechanics itself.