The Markov gap in the presence of islands

Abstract

The Markov gap [1], namely the difference between reflected entropy and mutual information, is explicitly computed in the defect extremal surface model, JT gravity, and the generic 2d extremal black holes, in vacuum states. The phases that contain various island contributions are considered, and their existence is carefully checked. Moreover, we show explicitly how the Markov gap originates from the OPE coefficient of the boundary CFT. And, as a generalization of [1], the lower bound of the Markov gap is given by $$ \frac{C}{3} $$ C 3 log 2 times the number of EWCS boundaries on minimal surfaces. We propose a boundary way of counting the lower bound for the Markov gap, which states that the lower bound is given by $$ \frac{C}{3} $$ C 3 log 2 times the number of gaps between two boundary regions in vacuum states. We discuss the limitation and possible generalization of the boundary counting, and its relation to tripartite entanglement.

Reflected entropy for communicating black holes. Part I. Karch-Randall braneworlds

“…There are various fascinating future directions which can be investigated to obtain a better understanding of the mixed state entanglement structure in Hawking radiation. Following some recent developments in [149,161,162], it will be interesting to study other mixed state correlation measures and their corresponding Markov gaps. One may also extend the study of the present article to investigate the multipartite correlations where it is expected to observe the characteristics of the holographic Markov gap.…”

Entanglement negativity and defect extremal surface

“…On the other hand, the entanglement wedge cross section (dashed arc in fig. 15) is given by (see appendix A of [80]) . (B.12)…”

Binary AdS black holes coupled to a bath in Type IIB

“…Conversely, it would be interesting to study aspects which have been studied recently in bottom-up models in the top-down models, e.g. additional information-theoretic quantities [53][54][55][56][57][58][59][60][61][62][63], charged black holes [64][65][66][67], connections to bootstrap conditions [68][69][70][71][72][73] and effective brane description [74][75][76][77][78][79][80][81], more general dynamics [82][83][84][85][86], and connections to de Sitter space and cosmology [87][88][89][90][91][92][93][94][95][96][97].…”