Long-distance entanglement of purification and reflected entropy in conformal field theory

TL;DR

This paper investigates how entanglement of purification and reflected entropy decay with distance in conformal field theories, revealing a logarithmic enhancement over mutual information and providing numerical coefficients for specific models.

Contribution

It offers an elementary proof of the decay behavior of these entanglement measures and computes their coefficients in critical Ising and free fermion CFTs.

Findings

Decay of entanglement of purification and reflected entropy is logarithmically enhanced with distance.

Elementary proof of decay behavior in conformal field theories.

Numerical computation of coefficients for Ising and free fermion models.

Abstract

Quantifying entanglement properties of mixed states in quantum field theory via entanglement of purification and reflected entropy is a new and challenging subject. In this work, we study both quantities for two spherical subregions far away from each other in the vacuum of a conformal field theory in any number of dimensions. Using lattice techniques, we find an elementary proof that the decay of both, the entanglement of purification and reflected entropy, is enhanced with respect to the mutual information behaviour by a logarithm of the distance between the subregions. In the case of the Ising spin chain at criticality and the related free fermion conformal field theory, we compute also the overall coefficients numerically for the both quantities of interest.