Wehrl entropy of entangled Segal-Bargmann oscillators

TL;DR

This paper investigates the Wehrl entropy of entangled two-oscillator systems within the Segal-Bargmann space, providing insights into quantum uncertainty and entanglement quantification using phase-space methods.

Contribution

It introduces a novel analysis of Wehrl entropy for entangled oscillators in the Segal-Bargmann formalism, linking phase-space entropy with quantum entanglement measures.

Findings

Wehrl entropy quantifies entanglement in coupled oscillators.

Segal-Bargmann space simplifies Husimi function computation.

Mutual information reveals correlations between oscillators.

Abstract

In this manuscript we study the Wehrl entropy of entangled oscillators. This semiclassical entropy associated with the phase-space description of quantum mechanics can be used for formulating uncertainty relations and for a quantification of entanglement. We focus on a system of two coupled oscillators described within its Segal-Bargmann space. This Hilbert space of holomorphic functions integrable with respect to a given Gaussian-like measure is particularly convenient to deal with harmonic oscillators. Indeed, the Stone-von Neumann theorem allows us to work in this space in a full correspondence with the ladder operators formalism. In addition, the Husimi pseudoprobability distribution is directly computed within the Segal-Bargmann formalism. Once we obtain the Husimi function, we analyze the Wehrl entropy and mutual information.