# Reflected Entropy for Communicating Black Holes II: Planck Braneworlds

## TL;DR

This paper calculates the reflected entropy for bipartite mixed states in a finite-temperature CFT_2 setup with quantum dots, using both field theory and holographic methods, and explores its relation to entanglement wedge cross sections.

## Contribution

It provides a holographic derivation of reflected entropy for complex bipartite states involving quantum dots and confirms the duality with entanglement wedge cross sections.

## Key findings

- Reflected entropy matches entanglement wedge cross section in the dual bulk geometry.
- The holographic Markov gap varies with subsystem size and time.
- Results support the holographic duality in the $AdS_3/CFT_2$ context.

## Abstract

We obtain the reflected entropy for bipartite mixed state configurations of two adjacent and disjoint subsystems at a finite temperature in finite-sized non-gravitating reservoirs described by $CFT_2$s each coupled to two quantum dots at their boundaries in the large central charge limit through a replica technique. These field theory results are substantiated through a holographic computation involving the entanglement wedge cross section in the dual bulk BTZ black hole geometry truncated by two Planck branes. The two Planck branes are the holographic duals of the quantum dots described by $AdS_2$ slices with JT black holes. Our results reproduce the holographic duality between the reflected entropy and the bulk entanglement wedge cross section in the context of the $AdS_3/CFT_2$ correspondence. Subsequently we analyze the behaviour of the holographic Markov gap between the reflected entropy and the mutual information for different scenarios involving the subsystem sizes and time.