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

Abstract

We obtain the reflected entropy for bipartite mixed state configurations of two adjacent and disjoint intervals at a finite temperature in $BCF{T}_2$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 $Ad{S}_3/BCF{T}_2$ 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.

68 pages, 42 figures, 2 appendices

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• Entanglement inside a black hole before the Page time
• Compactified extra dimension and entanglement island as clues to quantum gravity
• Effect of backreaction on Island, Page curve and Mutual Information
• Renyi reflected entropy and entanglement wedge cross section with cosmic branes in AdS/BCFT