Complete condition for nonzero quantum correlation in continuous variable systems

TL;DR

This paper establishes a simple, necessary and sufficient condition for detecting nonzero quantum correlation in continuous variable systems using a new marker $Q_r$, applicable to Gaussian and non-Gaussian states.

Contribution

It introduces a novel criterion and marker $Q_r$ for quantum correlation in continuous variables, based on continuous-variable local orthogonal bases, facilitating easier detection.

Findings

The marker $Q_r$ applies to all bipartite continuous variable states.

The condition is both necessary and sufficient for nonzero quantum correlation.

Quantum circuits can measure the proposed quantum correlation measure.

Abstract

Quantum correlation provides a promising measure beyond entanglement. Here, we propose a necessary and sufficient condition for nonzero quantum correlation in continuous variable systems, which is simple and easy to perform in terms of a marker $Q_r$. In order to get this condition, we introduce continuous-variable local orthogonal bases of the operator space, which are generalized from the orthogonal basis sets in local operator space for discrete variables. Based on this, we obtain the marker $Q_r$ for all bipartite continuous variable states, and provide several examples including two-mode Gaussian and non-Gaussian states. Our result may provide a candidate for quantum correlation measures, and can be measured by designed quantum circuits.