Constructing local models for general measurements on bosonic Gaussian states

TL;DR

This paper presents a simple criterion for determining the locality of measurement correlations on Gaussian states, demonstrating that some entangled states can still admit local-hidden-variable models.

Contribution

It introduces a new sufficient condition for locality based on Gaussian noise transfer, applicable to measurements on Gaussian quantum states.

Findings

The criterion can identify local correlations in entangled Gaussian states.

It shows the existence of local-hidden-variable models for certain entangled states.

Applied to displaced photodetection, the criterion reveals local models for specific parameters.

Abstract

We derive a simple sufficient criterion for the locality of correlations obtained from given measurements on a Gaussian quantum state. The criterion is based on the construction of a local-hidden-variable model which works by passing part of the inherent Gaussian noise of the state onto the measurements. We illustrate our result in the setting of displaced photodetection on a two-mode squeezed state. Here, our criterion exhibits the existence of a local-hidden-variable model for a range of parameters where the state is still entangled.