In this note we discuss a topological realization of the quantum teleportation protocol. Such a realization facilitates keeping track of the evolution of quantum correlations in the system. It is then suggested, that an implementation of a similar protocol can serve as a toy model of a process of information transfer between causally disconnected regions, such as the one that should take place in a unitary evolution of a quantum black hole. Hawking quanta provide the necessary entangled pairs for the teleportation channel, and the same interaction mechanism that creates the Hawking pairs, destroys the entanglement at the late stages of the evolution. Different steps of the teleportation protocol are characterized by the entropies associated with the disconnected regions, and one can introduce an analog of the Page curve for the entropy of the Hawking radiation. Some regions of the “black hole” interior appear to actually encode the information of the exterior, so it is natural to identify them with the “islands” of the semiclassical gravity analysis.
In this note we discuss a topological realization of the quantum teleportation protocol. Such a realization facilitates keeping track of the evolution of quantum correlations in the system. It is then suggested, that an implementation of a similar protocol can serve as a toy model of a process of information transfer between causally disconnected regions, such as the one that should take place in a unitary evolution of a quantum black hole. Hawking quanta provide the necessary entangled pairs for the teleportation channel, and the same interaction mechanism that creates the Hawking pairs, destroys the entanglement at the late stages of the evolution. Different steps of the teleportation protocol are characterized by the entropies associated with the disconnected regions, and one can introduce an analog of the Page curve for the entropy of the Hawking radiation. Some regions of the “black hole” interior appear to actually encode the information of the exterior, so it is natural to identify them with the “islands” of the semiclassical gravity analysis.
Abstract 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, nevertheless, does not provide a concrete insight on how information comes out from a black hole. In this paper, we start from a qubit model and provide a quantum informational interpretation of entanglement islands. We propose an identification of entanglement islands with quantum measurements and remark on the parallel between the black hole information problem and the old problem of quantum measurements. We show that the Page curve can still be realized even if information is lost so that the information paradox can be explained as one manifestation of measurement problem. We show that such interpretation is necessary for a quantum informational model if smooth horizons and bulk reconstruction are assumed, and demonstrate explicitly that Page curves of solvable 2D gravity can be obtained through teleportation and entanglement swapping. We argue that the similarities between the black hole information problem and the measurement problem suggest links in the origins of the two problems.
This paper proposes that black holes can be described as globally coherent quantum systems, despite the emission of Hawking radiation. While the Hawking process induces a weak coupling between the interior and exterior regions, this interaction is demonstrated to be too small to produce significant decoherence for macroscopic and supermassive black holes. By treating the event horizon as a quasi-isolated, semi-transparent quantum interface, this framework reconciles semiclassical gravity with quantum unitarity. The black hole and its emitted radiation are modeled as a single, entangled pure quantum state that evolves unitarily. Key contributions of this work include: Formalization of the black hole-radiation system as a coherent quantum cavity. Mathematical derivation showing that the decoherence rate scales as Γ_dec ∝ M⁻⁸. Demonstration that for astrophysical black holes, the decoherence time τ_D is astronomically larger than the evaporation time t_evap, implying that global quantum coherence is effectively preserved. A potential resolution to the black hole information paradox within a unitary evolution framework. This research contributes to the ongoing theoretical discussion on the nature of event horizons, quantum information, and the holographic principle. Acknowledgements: I would like to express my deepest gratitude to my beloved dog, Milo, and my father, for their constant support, encouragement, and companionship throughout the development of this research.
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.
Abstract Topological quantum field theories (TQFT) encode properties of quantum states in the topological features of abstract manifolds. One can use the topological avatars of quantum states to develop intuition about different concepts and phenomena of quantum mechanics. In this paper we focus on the class of simplest topologies provided by a specific TQFT and investigate what the corresponding states teach us about entanglement. These “planar connectome” states are defined by graphs of simplest topology for a given adjacency matrix. In the case of bipartite systems the connectomes classify different types of entanglement matching the classification of stochastic local operations and classical communication (SLOCC). The topological realization makes explicit the nature of entanglement as a resource and makes apparent a number of its properties, including monogamy and characteristic inequalities for the entanglement entropy. It also provides tools and hints to engineer new measures of entanglement and other applications. Here the approach is used to construct purely topological versions of the dense coding and quantum teleportation protocols, giving diagrammatic interpretation of the role of entanglement in quantum computation and communication. Finally, the topological concepts of entanglement and quantum teleportation are employed in a simple model of information retrieval from a causally disconnected region, similar to the interior of an evaporating black hole.
The quantum description of a black hole predicts that quantum information hidden behind the event horizon can be teleported outside almost instantaneously. In this work, we demonstrate that a chiral spin-chain model, which naturally simulates a binary black hole system, can realise this teleportation process. Our system captures two essential components of this protocol: Hawking radiation, which generates the necessary entanglement between the black holes, and optimal scrambling, which enables high-fidelity teleportation on short timescales. Through numerical simulations, we quantify the key timescales governing the process, including the Page time, radiation time, scrambling time, and butterfly velocity, showing their universal dependence on the chiral coupling strength. Our results establish the feasibility of simulating quantum properties of black holes within condensed matter systems, offering an experimentally accessible platform for probing otherwise inaccessible high-energy phenomena.
The Island Formula for Quantum Extremal Surfaces of large AdS black holes, which are made to evaporate by coupling the CFT of the AdS/CFT correspondence to an external system, demonstrates that the space time picture can reproduce the quantum mechanically required Page curve of the CFT/bath system if a region in the interior of the black hole has become entangled with the external radiation by the Page time. In an effective quantum field theory (EFT) description in ``nice slice" coordinates, this appears to imply paradoxical entanglement between degrees of freedom that have been causally disconnected since long before the Page time. We will give two arguments that all of the quantum information in the island is in fact concentrated in a tiny space-like portion of the island very close to the black hole horizon at the Page time. The first applies the covariant entropy bound\cite{fsb} (CEB) to the causal diamonds of geodesics originating on the space-like region that becomes the island, but on a time slice just before the Page time. All points on the island except those in a stretched horizon region very close to the horizon have entropy bounds that are tiny fractions of the black hole entropy. The second argument uses standard quantum statistical mechanics combined with the tensor network renormalization group regularization of CFT to argue that the wave function of a typical pure state in the microcanonical evaporating black hole always has most of its probability concentrated in a small range of wavelengths corresponding to a small range of radii in the dual tensor network/AdS slice.