Abstract We study entanglement dynamics in toy models of black hole information built out of chaotic many-body quantum systems, by utilising a coarse-grained description of entanglement dynamics in such systems known as the ‘entanglement membrane’. We show that in these models the Page curve associated to the entropy of Hawking radiation arises from a transition in the entanglement membrane around the Page time, in an analogous manner to the change in quantum extremal surfaces that leads to the Page curve in semi-classical gravity. We also use the entanglement membrane prescription to study the Hayden-Preskill protocol, and demonstrate how information initially encoded in the black hole is rapidly transferred to the radiation around the Page time. Our results relate recent developments in black hole information to generic features of entanglement dynamics in chaotic many-body quantum systems.
Abstract We study entanglement dynamics in toy models of black hole information built out of chaotic many-body quantum systems, by utilising a coarse-grained description of entanglement dynamics in such systems known as the ‘entanglement membrane’. We show that in these models the Page curve associated to the entropy of Hawking radiation arises from a transition in the entanglement membrane around the Page time, in an analogous manner to the change in quantum extremal surfaces that leads to the Page curve in semi-classical gravity. We also use the entanglement membrane prescription to study the Hayden-Preskill protocol, and demonstrate how information initially encoded in the black hole is rapidly transferred to the radiation around the Page time. Our results relate recent developments in black hole information to generic features of entanglement dynamics in chaotic many-body quantum systems.
The quantum extremal island rule allows us to compute the Page curves of Hawking radiation in semi-classical gravity. In this work, we study the connection between these calculations and the thermalisation of chaotic quantum many-body systems, using a coarse-grained description of entanglement dynamics known as the entanglement membrane. Starting from a double-holographic model of eternal two-sided asymptotically AdSd (d>2) black hole each coupled to a flat d-dimensional bath, we show that the entanglement dynamics in the late-time, large-subregion limit is described by entanglement membrane, thereby establishing a quantitative equivalence between a semi-classical gravity and a chaotic quantum many-body system calculation of the Page curve.
A bstract If the evaporation of a black hole formed from a pure state is unitary, the entanglement entropy of the Hawking radiation should follow the Page curve, increasing from zero until near the halfway point of the evaporation, and then decreasing back to zero. The general argument for the Page curve is based on the assumption that the quantum state of the black hole plus radiation during the evaporation process is typical. In this paper, we show that the Page curve can result from a simple dynamical input in the evolution of the black hole, based on a recently proposed signature of quantum chaos, without resorting to typicality. Our argument is based on what we refer to as the “operator gas” approach, which allows one to understand the evolution of the microstate of the black hole from generic features of the Heisenberg evolution of operators. One key feature which leads to the Page curve is the possibility of dynamical processes where operators in the “gas” can “jump” outside the black hole, which we refer to as void formation processes. Such processes are initially exponentially suppressed, but dominate after a certain time scale, which can be used as a dynamical definition of the Page time. In the Hayden-Preskill protocol for young and old black holes, we show that void formation is also responsible for the transfer of information from the black hole to the radiation. We conjecture that void formation may provide a microscopic explanation for the recent semi-classical prescription of including islands in the calculation of the entanglement entropy of the radiation.
Abstract The role played by the mutual information of subsystems on the Page curve is explored in this paper. With the total system consisting of the black hole and radiation, together with the inclusion of island, we observe that the vanishing of mutual information between B+ B + and B− B - which in turn means the disconnected phase of the entanglement wedge corresponding to B+∪B− B + ∪ B - , yields a time scale of the order of scrambling time. This results in a time independent expression for the fine grained entropy of Hawking radiation consistent with the correct Page curve. We also find corrections to this entropy and Page time which are logarithmic and inverse power law in form.
Quantum computers are emerging technologies expected to become important tools for exploring various aspects of fundamental physics in the future. Therefore, we pose the question of whether quantum computers can help us to study the Page curve and the black hole information dynamics, which has been a key focus in fundamental physics. In this regard, we rigorously examine the qubit transport model, a toy qubit model of black hole evaporation on IBM’s superconducting quantum computers, to shed light on this question. Specifically, we implement the quantum simulation of the scrambling dynamics in black holes using an efficient random unitary circuit. Furthermore, we employ the swap-based many-body interference protocol and the randomized measurement protocol to measure the entanglement entropy of Hawking radiation qubits in this model. Finally, by incorporating quantum error mitigation techniques into our challenging implementation of entanglement entropy measurement protocols on the IBM quantum hardware, we accurately determine the Rényi entropy in the qubit transport model, thus showcasing the utility of quantum computers for future investigations of complex quantum systems.
The entanglement entropy of a black hole and that of its Hawking radiation are expected to follow the so-called Page curve: After an increase in line with Hawking’s calculation, it is expected to decrease back to zero once the black hole has fully evaporated, as demanded by unitarity. Recently, a simple system-plus-bath model has been proposed which shows a similar behavior. Here, we make a general argument as to why such a Page-curve-like entanglement dynamics should be expected to hold generally for system-plus-bath models at small coupling and low temperatures, when the system is initialized in a pure state far from equilibrium. The interaction with the bath will then generate entanglement entropy, but it eventually has to decrease to the value prescribed by the corresponding mean-force Gibbs state. Under those conditions, it is close to the system ground state. We illustrate this on two paradigmatic open-quantum-system models, the exactly solvable harmonic quantum Brownian motion and the spin-boson model, which we study numerically. In the first example we find that the intermediate entropy of an initially localized impurity is higher for more localized initial states. In the second example, for an impurity initialized in the excited state, the Page time—when the entropy reaches its maximum—occurs when the excitation has half decayed. Published by the American Physical Society 2024
This undergraduate dissertation was completed as part of the BSc Computer Science degree at Newcastle University in May 2026. It investigates whether Page-curve-like behaviour can be reproduced in a simplified computational model of black hole evaporation using concepts from quantum information theory.The black hole information paradox arises from an apparent conflict between Hawking radiation and the unitary evolution required by quantum mechanics. Rather than attempting to simulate the full physical dynamics of an evaporating black hole, this project models the black hole and its emitted radiation as two subsystems of a finite-dimensional multi-qubit quantum system. The aim is to explore the information-theoretic behaviour associated with the Page curve through computational modelling of entanglement entropy.The model was implemented in Python using NumPy and Matplotlib. Random pure quantum states are generated and represented using density matrices, after which partial trace operations are used to obtain the reduced density matrix of the radiation subsystem. The von Neumann entropy of this subsystem is then calculated as the proportion of the overall quantum system assigned to radiation increases. Repeated simulations are averaged to examine the evolution of entanglement entropy over normalised evaporation time.The project evaluates the model using Page-curve shape, estimated Page time, variation of a mass-like evaporation parameter, scaling across different system sizes, statistical stability across repeated simulations, and validation tests using known quantum states. The baseline simulation reproduces the characteristic rise, peak, and fall associated with the Page curve, with maximum radiation entropy occurring close to the midpoint of the normalised evolution. Simulations across different qubit counts also produce broadly consistent Page-curve-like behaviour.The results should be interpreted as a computational demonstration of entanglement-entropy behaviour under a simplified information-theoretic model rather than as a complete physical simulation of black hole evaporation. The model does not include spacetime geometry, quantum field dynamics, back-reaction, or Hamiltonian time evolution. Its purpose is instead to provide a transparent and reproducible computational representation of the relationship between subsystem partitioning, quantum entanglement, entropy, and the Page curve.This record contains the final undergraduate dissertation.Degree: BSc Computer Science Institution: Newcastle University Year: 2026 Supervisor: Dr Jonte HanceThis work is an undergraduate dissertation and has not been peer-reviewed as a journal publication.