Einstein-Podolsky-Rosen-like correlation on a coherent-state basis and inseparability of two-mode Gaussian states

TL;DR

This paper introduces a new criterion based on EPR-like uncertainties and state-overlap to detect entanglement in two-mode Gaussian states, with an experimental scheme for measurement.

Contribution

It proposes a novel separability condition using coherent-state-based EPR-like correlations and demonstrates its effectiveness for Gaussian entangled states.

Findings

The coherent-state-based condition detects Gaussian entanglement.

An experimental measurement scheme using heterodyne detection is proposed.

The method links EPR correlations to state separability in continuous variables.

Abstract

The strange property of the Einstein-Podolsky-Rosen (EPR) correlation between two remote physical systems is a primitive object on the study of quantum entanglement. In order to understand the entanglement in canonical continuous-variable systems, a pair of the EPR-like uncertainties is an essential tool. Here, we consider a normalized pair of the EPR-like uncertainties and introduce a state-overlap to a classically correlated mixture of coherent states. The separable condition associated with this state-overlap determines the strength of the EPR-like correlation on a coherent-state basis in order that the state is entangled. We show that the coherent-state-based condition is capable of detecting the class of two-mode Gaussian entangled states. We also present an experimental measurement scheme for estimation of the state-overlap by a heterodyne measurement and a photon detection with a feedforward operation.