Entanglement and Interface Conditions on Fields

TL;DR

This paper investigates how interface boundary conditions, specifically Robin conditions, influence the entanglement properties of a free scalar field, providing new insights into the structure of quantum entanglement in field theories.

Contribution

It introduces a method to analyze entanglement entropy under Robin boundary conditions and explores the impact of interface conditions on quantum entanglement measures.

Findings

Entanglement entropy varies with Robin parameter 

Conditional probability offers a new entanglement measure

Correlation functions provide an alternative way to compute the reduced density matrix

Abstract

We consider the vacuum wave function of a free scalar field theory in space partitioned into two regions, with the field obeying Robin conditions (of parameter $\kappa$) on the interface. A direct integration over fields in a subregion is carried out to obtain the reduced density matrix. This leads to a constructive proof of the Reeh-Schlieder theorem. We analyze the entanglement entropy as a function of the Robin parameter $\kappa$. We also consider a specific conditional probability as another measure of entanglement which is more amenable to analysis of the dependence on interface conditions. Finally, we discuss a direct calculation of correlation functions and how it gives an alternate route to the reduced density matrix.