General features of information transfer between quantum subsystems, via unitary evolution, are investigated, with applications to the problem of information transfer from a black hole to its surroundings. A particularly direct form of quantum information transfer is ``subsystem transfer,'' which can be characterized by the saturation of a subadditivity inequality. We also describe more general unitary quantum information transfer, and categorize different models for black hole evolution. Evolution that only creates paired excitations inside/outside the black hole is shown not to extract information, but information-transferring models exist both in the ``saturating'' and ``nonsaturating'' category. The former more closely capture thermodynamic behavior; the latter generically have an enhanced energy flux, beyond that of Hawking.
General features of information transfer between quantum subsystems, via unitary evolution, are investigated, with applications to the problem of information transfer from a black hole to its surroundings. A particularly direct form of quantum information transfer is subsystem transfer,'' which can be characterized by the saturation of a subadditivity inequality. We also describe more general unitary quantum information transfer, and categorize different models for black hole evolution. Evolution that only creates paired excitations inside/outside the black hole is shown not to extract information, but information-transferring models exist both in the saturating'' and ``nonsaturating'' category. The former more closely capture thermodynamic behavior; the latter generically have an enhanced energy flux, beyond that of Hawking.
The size of quantum information---or entanglement---transfer rates between subsystems is a generic question in problems ranging from decoherence in quantum computation and sensing, to quantum underpinnings of thermodynamics, to the behavior of quantum black holes. We investigate such rates for given couplings between subsystems, for sufficiently random subsystem evolution, and find evidence of a conjectured relation of these rates to the size of the couplings. This provides a direct connection between entanglement transfer and the microphysical couplings in the Hamiltonian that are responsible for it.
We study entanglement transfer in a minimal model of two qubits that are coupled with one another through an antiferromagnetic Heisenberg exchange (J~), and where one of them is additionally coupled to a fermionic environment through another antiferromagnetic Heisenberg exchange (JK). By tuning the coupling ratio JK/J~, the system undergoes a quantum phase transition at T=0, accompanied by a redistribution of entanglement from the d′−d qubit-subsystem to the environment. Remarkably, the resulting physics exhibits properties that bear analogy with a quantum-information theoretic perspective of the physics of black hole thermodynamics. Carefully selected bipartite and tripartite mutual information measures displays behaviour analogous to the dynamical evolution of black hole entropy, Hawking entropy, and the Page curve expected during the process of evaporation. An effective temperature scale is obtained from the variation of the ground state energy with respect to changes in the bipartite mutual information between the subsystem and the bath. A steady growth of this temperature with the coupling ratio resembles that of the Hawking temperature with the inverse mass of the black hole. Concomitantly, the emergence of non-Fermi liquid behaviour observed near the quantum critical point and in the strong-coupling phase resembles strange-metal-like physics expected near the event horizon from a holographic duality perspective. Our results establish the minimal model as a platform for studying entanglement transfer and information scrambling within a fully unitary quantum framework, and offer new insights into a resolution of the black hole information paradox.
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 mechanics. Although the AdS/CFT correspondence indicates that information is preserved during black hole evaporation, the precise mechanism by which it is recovered from the Hawking radiation remains an open question. To explore a potential resolution, we investigate information transfer in a spin-chain model featuring an effective horizon realized via position-dependent couplings within an XY spin chain. We derive and demonstrate Page curve-like behavior, and analyze the transmission of quantum resources, such as entanglement and coherence, across the effective horizon. Our results show that quantum resources initially localized within an interior subsystem can be transferred to the exterior via particle radiation through the horizon. This study provides a novel perspective from quantum simulation on how information may escape from black holes, thereby contributing to the further understanding of the black hole information paradox.
This review paper is intended for scholars with different backgrounds, possibly in only one of the subjects covered, and therefore little background knowledge is assumed. The first part is an introduction to classical and quantum information theory (CIT, QIT): basic definitions and tools of CIT are introduced, such as the information content of a random variable, the typical set, and some principles of data compression. Some concepts and results of QIT are then introduced, such as the qubit, the pure and mixed states, the Holevo theorem, the no-cloning theorem, and the quantum complementarity. In the second part, two applications of QIT to open problems in theoretical physics are discussed. The black hole (BH) information paradox is related to the phenomenon of the Hawking radiation (HR). Consid- ering a BH starting in a pure state, after its complete evaporation only the Hawking radiation will remain, which is shown to be in a mixed state. This either describes a non-unitary evolution of an isolated system, contradicting the evolution postulate of quantum mechanics and violating the no-cloning theorem, or it implies that the initial information content can escape the BH, therefore contradicting general relativity. The progress toward the solution of the paradox is discussed. The renormalization group (RG) aims at the extraction of the macroscopic description of a physical system from its microscopic description. This passage from microscopic to macroscopic can be described in terms of several steps from one scale to another, and is therefore formalized as the action of a group. The c-theorem proves the existence, under certain conditions, of a function which is monotonically decreasing along the group transformations. This result suggests an interpretation of this function as entropy, and its use to study the information flow along the RG transformations.
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.
The purpose of this paper is to analyze, in the light of information theory and with the arsenal of (elementary) quantum mechanics (EPR, correlations, copying machines, teleportation, mixing produced in subsystems owing to a trace operation, etc.) the scenarios available on the market to resolve the so-called black hole information paradox. We shall conclude that the only plausible ones are those where either the unitary evolution of quantum mechanics is given up, in which information leaks continuously in the course of black hole evaporation through nonlocal processes, or those in which the world is polluted by an infinite number of metastable remnants.