Islands and Uhlmann phase: explicit recovery of classical information from evaporating black holes

Abstract

Recent work has established a route towards the semiclassical validity of the Page curve, and so provided evidence that information escapes an evaporating black hole. However, a protocol to explicitly recover and make practical use of that information in the classical limit has not yet been given. In this paper, we describe such a protocol, showing that an observer may reconstruct the phase space of the black hole interior by measuring the Uhlmann phase of the Hawking radiation. The process of black hole formation and evaporation provides an invertible map between this phase space and the space of initial matter configurations. Thus, all classical information is explicitly recovered. We assume in this paper that replica wormholes contribute to the gravitational path integral.

Edge modes as reference frames and boundary actions from post-selection

“…This problem has received renewed interest in recent years [11,[66][67][68], in part because of its relevance to holography, e.g. see [37,[69][70][71][72][73][74][75][76][77][78], gravitational observables [79], and more generally, to the characterization of asymptotic symmetries in gauge and gravitational subsystems, see e.g. [28,35,68,[80][81][82][83][84][85][86][87].…”

C${\cal C}$osmological G${\cal G}$eometric P${\cal P}$hase F${\cal F}$rom P${\cal P}$ure Q${\cal Q}$uantum S${\cal S}$tates: A Study without/ with having Bell's Inequality Violation

“…">Normalization Condition: $${\cal F}(\rho ,\rho )=1$$. Invariance under Unitary transformation: $${\cal F}(\rho ,\sigma )\, \, \, \xrightarrow []{{\cal U}}\, \, \, \widetilde{{\cal F}(\rho ,\sigma )}:={\cal F}({\cal U}\rho {\cal U}^{\dagger },{\cal U}\sigma {\cal U}^{\dagger })={\cal F}(\rho ,\sigma )$$ where $${\cal U}$$ is the Unitary operator. The most important outcome is in this computation for the mixed quantum states a generalized geometric phase arises, which is known as the Uhlmann phase [ 3,109–114 ] which can be expressed in terms of Fidelity by the following expression: $$\begin{eqnarray} \gamma _{\rm Uhlmann}:={\rm arg}{\left[{\left({\rm Tr}{\left[\, \sqrt {\rho }\, \sigma \, \sqrt {\rho }\, \right]}\right)}\right]}=\sqrt {{\cal F}(\rho ,\sigma )}.\end{eqnarray}$$In future it is possible to generalize the present computation for mixed states in primordial cosmological perturbation theory set up and it be really interesting explicitly find the corresponding Uhlmann phase [ 3,109–114 ] from the computation of Fidelity . Additionally, for this extended mixed state framework one can further study the relationship among Uhlmann phase , quantum speed limit and the trace distance which gives an additional constraint: …”

“…There are two possible phases appearing in the present literature, A. Pancharatnam Berry phase for the pure quantum states [ 1,2,5–7 ] and B. Uhlmann phase for the mixed quantum states. [ 3,109–114 ] 7.Quantification of correlations when out‐of‐equilibrium aspects are dominant and this can be done using the concept of out‐of‐time‐ordered‐correlation (OTOC) functions.…”