Entanglement and separability in the noncommutative phase-space scenario

TL;DR

This paper explores how noncommutative phase-space deformation can induce entanglement in Gaussian states, revealing that noncommutativity alone can generate quantum correlations in continuous variable systems.

Contribution

It demonstrates that noncommutative deformation of covariance matrices can induce entanglement, providing new insights into quantum correlations in noncommutative phase-space.

Findings

Entanglement can be generated solely by noncommutative deformation.

Standard quantum mechanics separable states can become entangled under NC deformation.

Positive partial transpose criterion is used to identify entanglement in NC Gaussian states.

Abstract

Quantumness and separability criteria for continuous variable systems are discussed for the case of a noncommutative (NC) phase-space. In particular, the quantum nature and the entanglement configuration of NC two-mode Gaussian states are examined. Two families of covariance matrices describing standard quantum mechanics (QM) separable states are deformed into a NC QM configuration and then investigated through the positive partial transpose criterium for identifying quantum entanglement. It is shown that the entanglement of Gaussian states may be exclusively induced by switching on the NC deformation. Extensions of some preliminary results are presented.