Entanglement in phase-space distribution for an anisotropic harmonic oscillator in noncommutative space

TL;DR

This paper investigates entanglement in a bipartite Gaussian state of an anisotropic harmonic oscillator in noncommutative space, revealing conditions for entanglement and identifying entangled degrees of freedom via phase-space analysis.

Contribution

It provides exact solutions and criteria for entanglement in noncommutative harmonic oscillators, linking phase-space distributions to entanglement detection.

Findings

Entanglement occurs only between coordinates and conjugate momenta of different degrees of freedom.

A unique constraint relates system parameters for entanglement to manifest.

Phase-space analysis via Wigner distribution identifies entangled degrees of freedom.

Abstract

The bi-partite Gaussian state, corresponding to an anisotropic harmonic oscillator in a noncommutative-space, is investigated with the help of the Simon's separability condition (generalized Peres-Horodecki criterion). It turns out that, in order to exhibit the entanglement between the noncommutative co-ordinates, the parameters (mass and frequency) have to satisfy an unique constraint equation. Exact solutions for the system are obtained after diagonalizing the model, keeping the intrinsic symplectic structure intact. It is shown that, the identification of the entangled degrees of freedom is possible by studying the Wigner quasiprobability distribution in phase-space. We have shown that the co-ordinates are entangled only with the conjugate momentum corresponding to other co-ordinates.