Hawking's black hole evaporation process suggests that we may need to choose between quantum unitarity and other basic physical principles such as no-signaling, entanglement monogamy, and the equivalence principle. We here show that the Hawking's quantum model for the black hole evaporation is consistent with the above fundamental principles. Our analysis does not involve exotic new physics, but rather uses standard quantum theory, general relativity, and the Einstein–Hilbert action including matter. We explicitly show that the whole state consisting of matter and radiation (in a joint superposition of different energy states) is pure at any stage of the evaporation process, including the particular case of 0 mass. Moreover, after full evaporation the state for radiation at infinity is pure and in one-to-one correspondence with the initial state forming the black hole. Thus there is no information loss upon full evaporation according to the quantum information theory. The original entanglement of the black hole matter (if any) gets transferred to the outgoing particles via a process similar to entanglement swapping, without violation of causality (as proved explicitly). On the other hand, if the initial state is a tensor product state, the entanglement of Hawking particles, present in the intermediate phase, is broken when the black hole evaporates completely. Therefore, the final state (entangled or tensor product depending on the nature of initial state) after the full black hole evaporation is pure without loss of information.
A bstract We use hyperbolic tensor networks to construct a holographic map for black hole interiors that adds a notion of locality to the non-isometric codes proposed by Akers, Engelhardt, Harlow, Penington, and Vardhan. We use tools provided by these networks to study the relationship between non-isometries and quantum extremal surfaces behind the horizon. Furthermore, we introduce a limited notion of dynamics for these interior tensor networks based on the qudit models introduced by Akers et al., and study the evolution of quantum extremal surfaces in an evaporating black hole. We also find a tensor network description of a wormhole connecting the black hole interior to the radiation, providing a mechanism for interior states and operators to be encoded in the radiation after the Page time. As a particular case, we construct a tensor network realization of the backwards-forwards maps recently proposed to incorporate non-trivial effective dynamics in dynamical constructions of these non-isometric black hole codes.
Abstract A general structure of unitary evolution (evaporation) of the black hole, respecting causality imposed by the event horizon (semicausality), has been derived and presented in the language of quantum circuits. The resulting consequences for the evolution of the corresponding entanglement entropy and the entropy curve have been determined. As an illustration of the general scheme, two families of qubit toy models have been discussed: tensor product models and controlled non-product models.
In this work, we study the distinguishability of random states drawn from the Wishart ensemble as well as black hole microstates.We compute the relative entropy and many generalizations, including the Petz Rényi relative entropy, sandwiched Rényi relative entropy, fidelities, and trace distances.These generalized quantities are able to teach us about new structures in the space of random states and black hole microstates where the von Neumann and relative entropies were insufficient.We further generalize to generic random tensor networks where new phenomena arise due to the locality in the networks.These phenomena sharpen the relationship between holographic states and random tensor networks.We discuss the implications of our results on the black hole information problem using replica wormholes, specifically the state dependence (hair) in Hawking radiation.Understanding the differences between Hawking radiation of distinct evaporating black holes is an important piece of the information problem that was not addressed by entropy calculations using the island formula.We interpret our results in the language of quantum hypothesis testing and the subsystem eigenstate thermalization hypothesis (ETH), deriving that chaotic (including holographic) systems obey subsystem ETH for all subsystems less than half the total system size.
Abstract We reexamine the quantum circuit model of black hole evaporation proposed in a previous work (Class. Quantum Grav. 35, 235013, 2018) [1]. This tripartite model incorporates the following systems: black hole (
BH BH ), just radiation (
JR JR ), and early radiation (
ER ER ). We apply a scrambling unitary matrix with a single parameter
θ θ to the ground state of the qubits in infalling matter toward a black hole in order to generate initial qubit states of the black hole that are more general than those in [1]. Specifically, the scrambling unitary matrix reduces to no scrambling and maximum scrambling when
θ=0 θ = 0 and
θ=π/2 θ = π / 2 , respectively. Our aim is to explore the role of quantum monogamy in the firewall formation between the black hole and radiation. In this model, entanglement and firewall formation depend on the black hole mass M and the frequency of Hawking radiation
ω ω . For the initial state with
θ=π/2 θ = π / 2 , a firewall emerges at an earlier stage of the evolution than with
θ=0 θ = 0 . We also find that a firewall structure emerges between
BH BH and
JR JR , and that the information is carried away by radiation for all values of
Mω M ω , provided that
θ θ lies within a certain analytically determined range. Following unitary gate dynamics, the initial black hole qubit state can be retrieved from its imprint on the final radiation state, which was originally hidden behind the black hole’s horizon. These results may provide insight into the properties of multipartite entanglement due to the different initial states in the evolution of a quantum circuit model for black hole evaporation.
Black hole evaporation is one of the most striking phenomena at the interface between gravity and quantum physics. In Hawking's semi-classical treatment, where matter is quantum mechanical and the spacetime is definite and classical, evaporation leads to an apparent loss of unitarity of the overall evolution, and to the so-called black hole information paradox. Here, we go beyond this semi-classical treatment and formulate a toy quantum model of black hole evaporation that allows the black hole to evolve into a superposition of being fully evaporated and not fully evaporated, consistent with the Hawking particles being in a coherent superposition of different energy levels. We model Hawking particle production by the repeated action of quantum-controlled unitaries, generating emission from the quantum black hole and accounting for a quantum coherent back-reaction on the black hole matter state. We show that the probability of full annihilation of the black hole matter increases with time until the black hole is, asymptotically, fully evaporated in every branch of the quantum superposition. We prove that under natural assumptions, this evaporation model is unitary, such that the initial state can in principle be recovered from the final asymptotic state of the radiation.