Replica wormholes and holographic entanglement negativity

Abstract

Recent work has shown how to understand the Page curve of an evaporating black hole from replica wormholes. However, more detailed information about the structure of its quantum state is needed to fully understand the dynamics of black hole evaporation. Here we study entanglement negativity, an important measure of quantum entanglement in mixed states, in a couple of toy models of evaporating black holes. We find four phases dominated by different types of geometries: the disconnected, cyclically connected, anti-cyclically connected, and pairwise connected geometries. The last of these geometries are new replica wormholes that break the replica symmetry spontaneously. We also analyze the transitions between these four phases by summing more generic replica geometries using a Schwinger-Dyson equation. In particular, we find enhanced corrections to various negativity measures near the transition between the cyclic and pairwise phase.

Entanglement negativity and defect extremal surface

“…Last, compare our negativity curve to those in other models. For instance, there are recent studies of negativity in JT+EOW models of evaporating black holes [58]. It would be interesting to compare these results.…”

Mixed-state entanglement and information recovery in thermalized states and evaporating black holes

“…This problem is studied systematically in ref. [56]. For the special case of the "microcanonical ensemble" in [4], the equation for the resolvent reduces to the infinite temperature case in (C.8), with the dimension of the black hole given by e S , where S is the microcanonical entropy of the black hole.…”

“…Figure 20. For n = 6 and τ = (12)(34)(56), we show the planar double-line diagrams and the corresponding polygons that we get for the first and third terms in the second line of (A.6), using the boundary conditions from (19) (a) and (c).…”

Reflected entropy and entanglement negativity for holographic moving mirrors

“…The structure of mixed state entanglement in Hawking radiation seems to contain rich phase information which requires further investigations in the various black hole evaporation models [9,73,94,102,110]. It would be quite interesting to investigate this significant issue to elucidate our understanding of the information recovery from the black hole interior.…”

“…Specifically the reflected entropy and the entanglement negativity which are of interest in the present article have been shown to possess rich entanglement phase structures and are expected to lead to corresponding analogues of the Page curves [41,[147][148][149] for black hole/bath systems. Furthermore, recently the island formulae for the reflected entropy and the entanglement negativity have been proposed and explored in [19,20,48,73,150].…”