Including contributions from entanglement islands to the reflected entropy

Abstract

Recent work has demonstrated the need to include contributions from entanglement islands when computing the entanglement entropy in quantum field theory states coupled to regions of semiclassical gravity. We propose a new formula for the reflected entropy that includes additional contributions from such islands. We derive this formula from the gravitational path integral by finding additional saddles that include generalized replica wormholes. We also demonstrate that our covariant formula satisfies all the inequalities required of the reflected entropy. We use this formula in various examples that demonstrate its relevance in illustrating the structure of multipartite entanglement that are invisible to the entropies.

Quantum extremal islands made easy. Part II. Black holes on the brane

“…have the RT surface anchored in the unphysical region behind the brane. 36 In particular then, no islands form with λ b > 1 in the regime of interest with θ B ≤ π/2.…”

“…Since the former diverges negatively while the latter diverges positively, it follows that there exists a critical angle θ c for which 36 The physical significance of 34 Of course, this was our regime of interest, as this was the regime where a (nearly) massless graviton is induced on the brane. 35 Specifically, this can be seen as follows: let us take the extreme case of λ b = 1 (λ b = −1).…”

Evaporating black holes coupled to a thermal bath

“…In the present context, the phase transition where the QEIs appear corresponds to the time when the thermal bath encodes (part of) the black hole interior, a manifestation of the ER = EPR principle [18]. See [16,17,[19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] for recent explorations on the island formula in different black hole geometries and [33,[36][37][38][39][40][41][42][43][44][45][46][47][48] for more associated studies on information paradox and Page curve from various aspects.…”

Information transfer with a gravitating bath

“…Most work on islands in higher dimensions [9,[12][13][14][15][16][22][23][24][25][26], as well as some of the results in lower dimensions [27][28][29][30][31][32], have been obtained in the context of the Randall-Sundrum (RS) braneworlds [33] with subcritical tension branes [34,35], also known as the Karch-Randall (KR) braneworlds. Compared to the generic RS setup, KR has several specific features.…”