Reflected Entropy for Communicating Black Holes I: Karch-Randall Braneworlds

TL;DR

This paper calculates the reflected entropy for bipartite states in BCFT_2 at finite temperature using replica techniques and confirms its holographic duality with the entanglement wedge cross section in a BTZ black hole geometry with Karch-Randall branes.

Contribution

It provides the first holographic computation of reflected entropy in BCFT_2 with two boundaries and explores the holographic Markov gap in braneworld geometries.

Findings

Reflected entropy matches the entanglement wedge cross section in the dual geometry.

Holographic Markov gap varies with subsystem size and time.

Results support the holographic duality in BCFT_2 scenarios.

Abstract

We obtain the reflected entropy for bipartite mixed state configurations of two adjacent and disjoint intervals at a finite temperature in $BCFT_2$s with two distinct boundaries through a replica technique in the large central charge limit. Subsequently these field theory results are reproduced from bulk computations involving the entanglement wedge cross section in the dual BTZ black hole geometry truncated by two Karch-Randall branes. Our result confirms the holographic duality between the reflected entropy and the bulk entanglement wedge cross section in the context of the $AdS_3/BCFT_2$ scenario. We further investigate the critical issue of the holographic Markov gap between the reflected entropy and the mutual information for these configurations from the bulk braneworld geometry and study its variation with subsystem sizes and time.