All non-locally Realized Continuous Variable Bipartite Gaussian States are Entangled

TL;DR

This paper explores the relationship between entanglement and non-locality in continuous-variable bipartite Gaussian states, showing that while entanglement is necessary for non-locality, it is not sufficient, but non-locality guarantees entanglement.

Contribution

It establishes a formal connection between entanglement and non-locality in continuous-variable Gaussian states using phase-space Wigner representation.

Findings

Entanglement is necessary but not sufficient for non-locality.

Non-locality guarantees entanglement in these states.

Non-locally realized Gaussian states are always entangled.

Abstract

We investigate the connection between entanglement and non-locality between continuous-variable bipartite Gaussian states. The investigation initiates with formulating non-locality by using the phase-space Wigner representation of Bell's function. Furthermore, our analysis shows entanglement to be necessary for nonlocality, but not sufficient for it; however, nonlocality is sufficient to ensure entanglement.