The Page Curve for Reflected Entropy

Abstract

We study the reflected entropy S R in the West Coast Model, a toy model of black hole evaporation consisting of JT gravity coupled to end-of-the-world branes. We demonstrate the validity of the holographic duality relating it to the entanglement wedge cross section away from phase transitions. Further, we analyze the important non-perturbative effects that smooth out the discontinuity in the S R phase transition. By performing the gravitational path integral, we obtain the reflected entanglement spectrum analytically. The spectrum takes a simple form consisting of superselection sectors, which we interpret as a direct sum of geometries, a disconnected one and a connected one involving a closed universe. We find that area fluctuations of O( √ G N ) spread out the S R phase transition in the canonical ensemble, analogous to the entanglement entropy phase transition. We also consider a Renyi generalization of the reflected entropy and show that the location of the phase transition varies as a function of the Renyi parameter.

Entanglement negativity, reflected entropy, and anomalous gravitation

“…Finally we note that it will be interesting to explore the holographic duality between the reflected entropy and the minimal EWCS in the framework of TMG-AdS 3 /CFT a 2 from a gravitational path integral perspective, similar to that in [20,76].…”

Large and Small Corrections to the JLMS Formula from Replica Wormholes

“…This behaviour has already been seen in the Renyi entropies for n < 1 in Refs. [31,35]. 8 For this phenomenon to occur, one only needs the number of accessible eigenstates in the black hole spectrum to be much larger than e S BH and not necessarily infinite.…”

“…Thus, the boundary relative entropy is finite while the bulk relative entropy is infinite for distinct pure states. contributions [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. We are therefore motivated to revisit the calculation of the relative entropy using the path integral and analyze corrections to the qJLMS formula.…”

Reflected entropy is not a correlation measure

“…The connection between reflected entropy and tripartite entanglement was studied further in [4], where the authors considered the structure of states with reflected entropy equal to the mutual information, and in [5], where the authors gave an interpretation of the reflected entropy in terms of an information-theoretic reconstruction problem. A great deal of work has been done to explore the physical properties of the reflected entropy in various systems of interest, including holographic models in [3,[5][6][7][8][9][10][11][12][13][14] and many-body systems in [4,[15][16][17][18][19][20][21][22][23][24][25][26][27][28]. None of these explorations, however, answers a basic physical question: does the magnitude of S R,ρ (A : B) quantify the magnitude of the correlations between systems A and B in the state ρ AB ?…”