Nonclassicality in phase space and nonclassical correlation

TL;DR

This paper investigates the relationship between nonclassicality and entanglement in continuous variable quantum states, identifying conditions under which nonclassicality can serve as an entanglement criterion, especially for Gaussian states.

Contribution

It clarifies the link between nonclassicality and entanglement, showing classical subsystems do not guarantee overall nonclassicality, and specifies local unitaries needed for Gaussian states.

Findings

Classical subsystems do not imply overall nonclassicality.

Local unitaries can establish equivalence between nonclassicality and entanglement in Gaussian states.

Quantitative relation between nonclassicality and entanglement analyzed.

Abstract

Continuous variable entanglement is a manifestation of nonclassicality of quantum states. In this paper we attempt to analyze whether and under which conditions nonclassicality can be used as an entanglement criterion. We adopt the well-accepted definition of nonclassicality in the form of lack of well-defined positive Glauber Sudarshan P-function describing the state. After demonstrating that the classicality of subsystems is not sufficient for the nonclassicality of the overall state to be identifiable with entanglement, we focus on Gaussian states and find specific local unitary transformations required to arrive at this equivalency. This is followed by the analysis of quantitative relation between nonclassicality and entanglement.