Entanglement entropy of dispersive media from thermodynamic entropy in one higher dimension

TL;DR

This paper links the entanglement entropy of dispersive media with thermodynamic entropy in a higher dimension, providing a new approach to compute quantum mutual information and revealing a logarithmic correction to the area law.

Contribution

It introduces a novel mapping between quantum mutual information in D dimensions and classical thermodynamic entropy in D+1 dimensions, simplifying analysis of entanglement.

Findings

Mutual information can be computed via classical thermodynamics in one higher dimension.

Logarithmic correction to the area law at short separations in 2D.

Method allows easy verification of strong subadditivity.

Abstract

A dispersive medium becomes entangled with zero-point fluctuations in the vacuum. We consider an arbitrary array of material bodies weakly interacting with a quantum field and compute the quantum mutual information between them. It is shown that the mutual information in D dimensions can be mapped to classical thermodynamic entropy in D+1 dimensions. As a specific example, we compute the mutual information both analytically and numerically for a range of separation distances between two bodies in D=2 dimensions and find a logarithmic correction to the area law at short separations. A key advantage of our method is that it allows the strong subadditivity property---notoriously difficult to prove for quantum systems---to be easily verified.