Investigating the Araki-Uhlmann relative entropy between two coherent states in relativistic Quantum Field Theory

TL;DR

This paper presents a numerical method to compute the Araki-Uhlmann relative entropy between coherent states in a 1+1 dimensional quantum field theory, confirming known properties and exploring how it varies with parameters.

Contribution

It introduces a numerical setup for calculating the relative entropy between coherent states in relativistic QFT, verifying known properties and analyzing parameter dependencies.

Findings

Relative entropy is positive and increases with region size.

It decreases as the mass parameter increases.

Relative entropy grows linearly with spatial distance between regions.

Abstract

A numerical setup for investigating the Araki-Uhlmann relative entropy between two coherent states is presented for a scalar massive Quantum Field Theory in ($1+1$)-dimensional Minkowski spacetime. These states are constructed using smeared Weyl operators compactly supported in two diamond regions belonging to the right Rindler wedge. Using this setup, we verified the known properties of the relative entropy, namely: positivity, increase with the size of the spacetime regions considered, decrease with the increase of the mass parameter. A linear increase with respect to the spatial distance between the two diamond regions is also observed.