The Einstein-Podolsky-Rosen Paradox and Entanglement 1: Signatures of EPR correlations for continuous variables

TL;DR

This paper generalizes the EPR paradox criteria for continuous variables, establishing conditions for demonstrating EPR correlations and their relation to entanglement, even without Bell inequality violations.

Contribution

It introduces new criteria for EPR correlations applicable to imperfect correlations and links these to entanglement verification in continuous variable systems.

Findings

Two types of EPR criteria based on variances and local realism are proposed.

Demonstrating EPR correlations implies entanglement in continuous variable systems.

Two-mode squeezing with spatially separated detectors indicates both entanglement and EPR correlations.

Abstract

A generalization of the 1935 Einstein-Podolsky-Rosen (EPR) argument for measurements with continuous variable outcomes is presented to establish criteria for the demonstration of the EPR paradox, for situations where the correlation between spatially separated subsystems is not perfect. Two types of criteria for EPR correlations are determined. The first type are based on measurements of the variances of conditional probability distributions and are necessary to reflect directly the situation of the original EPR paradox. The second weaker set of EPR criteria are based on the proven failure of (Bell-type) local realistic theories which could be consistent with a local quantum description for each subsystem. The relationship with criteria sufficient to prove entanglement is established, to show that any demonstration of EPR correlations will also signify entanglement. It is also shown how a demonstration of entanglement between two spatially separated subsystems, if not able to interpreted as a violation of a Bell-type inequality, may be interpreted as a demonstration of the EPR correlations. In particular it is explained how the experimental observation of two-mode squeezing using spatially separated detectors will signify not only entanglement but EPR correlations defined in a general sense.