Reflected Entropy for an Evaporating Black Hole

Abstract

We study reflected entropy as a correlation measure in black hole evaporation. As a measure for bipartite mixed states, reflected entropy can be computed between black hole and radiation, radiation and radiation. We compute reflected entropy curves in three different models: 3-side wormhole model, End-of-the-World (EOW) brane model in three dimensions and twodimensional eternal black hole plus CFT model. For 3-side wormhole model, we find that reflected entropy is dual to island cross sections. The reflected entropy between radiation and black hole increases at early time and then decreases to zero, similar to Page curve, but with a later transition time. The reflected entropy between radiation and radiation first increases and then saturates. For the EOW brane model, similar behaviors of reflected entropy are found.We propose a quantum extremal surface for reflected entropy, which we call quantum extremal cross section. In the eternal black hole plus CFT model, we find a generalized formula for reflected entropy with island cross section as its area term by considering the right half as the canonical purification of the left. Interestingly, the reflected entropy curve between the left black hole and the left radiation is nothing but the Page curve. We also find that reflected entropy between the left black hole and the right black hole decreases and goes to zero at late time. The reflected entropy between radiation and radiation increases at early time and saturates at late time.

Wormholes and holographic decoherence

“…We first discuss an explicit example in section 3.1 and then move to a more general argument 3.2. The discussion in this section is very similar to the one found in [31,32] where the entanglement between a black hole and Hawking radiation was studied using such multiboundary wormholes.…”

“…This four boundary wormhole is dual to a pure state on ABA B with interesting entanglement structure [28]. Other previous studies on entanglement in the class of multiboundary worm holes include [29][30][31][32]. By tracing out the thermal bath A B , we in general obtain a mixed state on AB.…”

Quantum Extremal Islands Made Easy, Part II: Black Holes on the Brane

“…(5.15) indicates that for θ B < π/2, sensible extremal surfaces intersecting the brane can only possibly exist when −1 < λ b < 1. 35 From figure 22a, we see that this is the range of λ b for which there exists some θ B < π/2 such that the DGP gradient has not overpowered the bulk term of eq. (5.14) to push the QES to the asymptotic boundary y = 0 or to the horizon y = ∞.…”

Topological reflected entropy in Chern-Simons theories

“…[15][16][17][18][19]. For further developments, we refer the reader to [20][21][22][23][24], while for candidates of multipartite reflected entropy, see [25][26][27].…”