Entanglement of Purification in Free Scalar Field Theories

TL;DR

This paper calculates the entanglement of purification in a 2D free scalar field theory, revealing its behavior at different distances and comparing it to holographic predictions, with implications for quantum correlations.

Contribution

It provides explicit numerical calculations of EoP in free scalar theories and explores its qualitative agreement with holographic conjectures at small distances.

Findings

EoP behaves like mutual information at large distances

EoP shows unique behavior at small distances matching holographic predictions

Violations of monogamy and strong superadditivity are observed

Abstract

We compute the entanglement of purification (EoP) in a 2d free scalar field theory with various masses. This quantity measures correlations between two subsystems and is reduced to the entanglement entropy when the total system is pure. We obtain explicit numerical values by assuming minimal gaussian wave functionals for the purified states. We find that when the distance between the subsystems is large, the EoP behaves like the mutual information. However, when the distance is small, the EoP shows a characteristic behavior which qualitatively agrees with the conjectured holographic computation and which is different from that of the mutual information. We also study behaviors of mutual information in purified spaces and violations of monogamy/strong superadditivity.