Masamichi Miyaji (UCB) “Islands Formula for Reflected Entropy” *ZOOM meeting ID 370 438 207* “BCTP String seminar”

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abst: We propose a new formula for a bi-partite correlation measure called reflected entropy, in the presence of evaporating black holes, or {\it entanglement islands}. Our new formula is written in terms of the reflected entropy of the bulk matter plus area term of a surface inside the entanglement island. We show that the measure shows interesting phase transition, which gives new information about multi-partite correlations between evaporating black holes and reservoir. We prove that our formula satisfies all the desired properties of the reflected entropy, and further give a derivation of the formula by using generalized replica wormhole. The derivation does not require the matter to be holographic, so in particular we do not need to assume additional higher dimensional holography.