Induced entanglement entropy of harmonic oscillators in noncommutative phase space

TL;DR

This paper investigates how noncommutative phase space affects entanglement entropy in harmonic oscillators, introducing a new Rènyi entropy definition and revealing entanglement effects due to noncommutativity.

Contribution

It proposes a novel Rènyi entropy based on Wigner functions for noncommutative phase space and demonstrates entanglement effects induced by noncommutativity.

Findings

Entanglement entropy depends on noncommutative parameters.

Harmonic oscillators can become entangled due to noncommutativity.

New entanglement-like effect caused by phase space noncommutativity.

Abstract

We study the entanglement entropy of harmonic oscillators in noncommutative phase space. We propose a new definition of quantum R\'enyi entropy based on Wigner functions in noncommutative phase space. Using the R\'enyi entropy, we calculate the entanglement entropy of the ground state of the 2D isotropic harmonic oscillators. We find that for some values of the noncommutative parameters, the harmonic oscillators can be entangled in noncommutative phase space. This is a new entanglement-like effect caused by the noncommutativity of the phase space.