Bell inequality violation and operator ordering in quantum theory

TL;DR

This paper explores how quantum operator ordering affects Bell inequality violations in two-photon polarization measurements, linking theoretical operator choices to experimental detection schemes and vacuum fluctuation contributions.

Contribution

It introduces a unified framework connecting operator ordering with density matrix representations and analyzes their impact on Bell tests and vacuum fluctuation effects.

Findings

Normal and symmetric operator orderings yield different Bell correlation predictions.

Vacuum fluctuations contribute to the detected signals and can be probed with new detection schemes.

Theoretical analysis bridges operator ordering choices with experimental observables.

Abstract

We investigate the role played by quantum operator ordering in the correlations that characterize two-photon polarization Bell measurements. The Clauser-Horne-Shimony-Holt (CHSH) criterion is investigated in the normal ordering imposed by the photodetection theory and in the symmetric ordering that constitutes the standard prescription for building Hermitian operators from products of noncommuting observables. The two approaches are obtained in a single theoretical framework, where operator ordering is directly associated with the representation used for the density matrix.Moreover, this discussion can be recast in terms of the contribution given by the vacuum fluctuations to the detected signals. We also envisage possible detection schemes sensitive to these fluctuations with recent technological developments.