Entanglement due to noncommutativity in the phase-space

TL;DR

This paper explores how noncommutative phase-space modifications can induce entanglement in Gaussian states, extending entanglement criteria and uncertainty relations to noncommutative quantum systems.

Contribution

It generalizes entanglement criteria and uncertainty relations to noncommutative phase-space, revealing that noncommutativity alone can induce entanglement in Gaussian states.

Findings

Entanglement can be induced solely by noncommutative deformation.

Generalization of entanglement criteria to noncommutative phase-space.

Noncommutative effects influence the separability of Gaussian states.

Abstract

The entanglement criterion for continuous variable systems and the conditions under which the uncertainty relations are fulfilled are generalized to the case of a noncommutative (NC) phase-space. The quantum nature and the separability of NC two-mode Gaussian states are examined. It is shown that the entanglement of Gaussian states may be exclusively induced by switching on the noncommutative deformation.