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Recent discovery of the fine-grained entropy formula in gravity succeeded in reconstructing the Page curves that are compatible with unitary evolution. The formula of generalized entropy derived from the gravitational path integration,…
We review recent progress on the information paradox. We explain why exponentially small correlations in the radiation emitted by a black hole are sufficient to resolve the original paradox put forward by Hawking. We then describe a…
This paper summarizes recent discussions of the Page curve and the information paradox, and responds to the reasoning and examples from arXiv:2506.04311. We review arguments demonstrating that in quantum gravity the algebra of observables…
Page curve for the fine grained entropy of the black hole radiation is obtained once we include the effect of a non vanishing quantum Fisher information in the evaporation data. This quantum Fisher information scales as the inverse of the…
The aim of this chapter is twofold. First, we introduce the information loss problem; second, we provide a critical assessment by thoroughly inspecting the assumptions underlying its formulations. In particular, we argue that if we work in…
In this paper, the information paradox on lower-dimensional Gauss-Bonnet gravity known as a three-dimensional EGB black hole is studied using the quantum extremal island approach. For that, we connect an auxiliary flat bath system to this…
The information loss paradox associated with black hole Hawking evaporation is an unresolved problem in modern theoretical physics. In this paper, we revisit the entanglement entropy via the Euclidean path integral (EPI) of the quantum…
It is known that the semiclassical approximation to the gravity path integral can be leveraged to explain certain inherently quantum aspects of gravity. One such aspect is the state-counting interpretation of the Bekenstein-Hawking entropy…
The information loss paradox is widely regarded as one of the biggest open problems in theoretical physics. Several classical and quantum features must be present to enable its formulation. First, an event horizon is needed to justify the…
Hawking's argument for information loss in black hole evaporation rests on the assumption of independent Hilbert spaces for the interior and exterior of a black hole. We argue that such independence cannot be established without…
The information loss paradox associated with black hole Hawking evaporation is an unresolved problem in modern theoretical physics. In a recent brief essay, we revisited the the evolution of the black hole entanglement entropy via the…
Hawking's black hole information puzzle highlights the incompatibility between our present understanding of gravity and quantum physics. However, Hawking's prediction of black-hole evaporation is at a semiclassical level. One therefore…
One-shot decoupling is a powerful primitive in quantum information theory and was hypothesized to play a role in the black hole information paradox. We study black hole dynamics modeled by a trilinear Hamiltonian whose semiclassical limit…
The black hole information paradox tells us something important about the way quantum mechanics and gravity fit together. In these lectures I try to give a pedagogical review of the essential physics leading to the paradox, using mostly…
The focusing theorem fails for evaporating black holes because the null energy condition is violated by quantum effects. The quantum focusing conjecture is proposed so that it is satisfied even if the null energy condition is violated. The…
Unitary evolution makes pure state on one Cauchy surface evolve to pure state on another Cauchy surface. Outgoing Hawking radiation is only subsystem on the late Cauchy surface. The requirement that Hawking radiation to be pure amounts to…
The complete evaporation of black holes, as a natural endpoint of Hawking radiation, gives rise to the black hole information paradox, which fundamentally challenges the principles of unitarity and information conservation in quantum…
We argue that the `island conjecture' and the replica wormhole derivation of the Page curve break monogamy of entanglement through allowing black hole interior states to be non-classically correlated while also pairwise entangled with…
In this invited review, we describe Hawking's information paradox and a recently proposed resolution of it. Explicit calculations demonstrate the existence of quantum hair on black holes, meaning that the quantum state of the external…
The aim of this work is to present the black hole information problem and discuss the assumptions and hypotheses necessary for its formulation. As the problem arises in the framework of semiclassical gravity, we first review the necessary…