The quantum information content of Hawking radiation holds the key to understanding black-hole evaporation and the fate of unitarity. Motivated by recent advances in cold-atom experiments, we develop a lattice-regularization approach aimed at simulating the coarse-grained entanglement scaling of a quantum field in a 1+1D analogue black-hole background. We provide the first concrete demonstration that logarithmic negativity -- an entanglement monotone that typically exhibits a UV-divergent log-scaling for the conformal vacuum -- acquires a UV-finite volume term from the nonlocal correlations seeded by Hawking radiation. We show that this volume term encodes both the number density and spatial distribution of entangled Hawking pairs along the black-hole interior and exterior. We highlight its prospective detection in currently realizable experiments as well as its implications beyond the analogue paradigm, in particular for black-hole thermodynamics.
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The quantum information content of Hawking radiation holds the key to understanding black-hole evaporation and the fate of unitarity. Motivated by recent advances in cold-atom experiments, we develop a lattice-regularization approach aimed at simulating the coarse-grained entanglement scaling of a quantum field in a 1+1D analogue black-hole background. We provide the first concrete demonstration that logarithmic negativity -- an entanglement monotone that typically exhibits a UV-divergent log-scaling for the conformal vacuum -- acquires a UV-finite volume term from the nonlocal correlations seeded by Hawking radiation. We show that this volume term encodes both the number density and spatial distribution of entangled Hawking pairs along the black-hole interior and exterior. We highlight its prospective detection in currently realizable experiments as well as its implications beyond the analogue paradigm, in particular for black-hole thermodynamics.
We theoretically study the entanglement of Hawking radiation pairs emitted by an analogue black hole. We find that this entanglement can be measured by the experimentally accessible density-density correlation function, vastly simplifying the measurement. We find that while the Hawking radiation exiting the black hole might be Planck-distributed, the correlations between the Hawking radiation and the partner particles has a distribution which is weaker but broader than Planckian. Thus, the high-energy tail of the distribution of Hawking radiation should be entangled, whereas the low-energy part should not be. This confirms previous studies. The full Peres-Horodecki criterion is considered, as well as a simpler criterion in the stationary, homogeneous case. Our method applies to systems which are sufficiently cold that the thermal phonons can be neglected.
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.
We study the mixed-state entanglement structure of chaotic quantum many-body systems at late times using the recently developed equilibrium approximation. A rich entanglement phase diagram emerges when we generalize this technique to evaluate the logarithmic negativity for various universality classes of macroscopically thermalized states. Unlike in the infinite-temperature case, when we impose energy constraints at finite temperature, the phase diagrams for the logarithmic negativity and the mutual information become distinct. In particular, we identify a regime where the negativity is extensive but the mutual information is subextensive, indicating a large amount of bound entanglement. When applied to evaporating black holes, these results imply that there is quantum entanglement within the Hawking radiation long before the Page time, although this entanglement may not be distillable into Einstein-Podolsky-Rosen pairs. We claim that at this earlier time, rather than the Page time, information about diaries thrown into the black hole first starts to leak out.
We introduce a method to numerically compute the entanglement entropy of an acoustic black hole. It is shown that the entanglement entropy of sufficiently large subregions scales linearly with size and thus shows a volume law instead of an area law. The origin of this scaling can be traced back to the non-separable long-distance correlations due to the production of phonon pairs at the horizon. The system is shown to be locally thermal, such that the part of the entanglement entropy scaling with volume is well approximated by the thermal entropy of the outgoing Hawking radiation.
We study the universal behavior of quantum information-theoretic quantities in thermalized isolated quantum many-body systems and evaporating black holes. In particular, we study a genuine mixed-state entanglement measure called the logarithmic negativity, other correlation measures including the Renyi negativities and the mutual information, and a signature of multipartite entanglement called the reflected entropy. We also probe the feasibility of recovering quantum information from subsystems of a thermalized quantum many-body system or from the radiation of an evaporating black hole, using quantities such as relative entropy and Petz map fidelity. A recently developed technique called the equilibrium approximation allows us to probe these quantities at finite temperature. We find striking qualitative differences from the infinite temperature case, which has been the topic of previous studies using Haar-random states. In particular, we find regimes where the logarithmic negativity is extensive but the mutual information is sub-extensive, indicating a large amount of undistillable, bound entanglement in thermalized states. For evaporating black holes at finite temperature, both the logarithmic negativity and the Petz map fidelity reveal an important new time scale tb, which is earlier than the Page time tp by a finite fraction of the total evaporation time. We find that tb, as opposed to tp, is the time scale at which quantum entanglement between different parts of the radiation becomes extensive, and the fidelity of information recovery for a large diary thrown into the black hole starts to grow.
Abstract We study the universal behavior of quantum information-theoretic quantities in thermalized isolated quantum many-body systems and evaporating black holes. In particular, we study a genuine mixed-state entanglement measure called the logarithmic negativity, other correlation measures including the Renyi negativities and the mutual information, and a signature of multipartite entanglement called the reflected entropy. We also probe the feasibility of recovering quantum information from subsystems of a thermalized quantum many-body system or from the radiation of an evaporating black hole, using quantities such as relative entropy and Petz map fidelity. A recently developed technique called the equilibrium approximation allows us to probe these quantities at finite temperature. We find striking qualitative differences from the infinite temperature case, which has been the topic of previous studies using Haar-random states. In particular, we find regimes where the logarithmic negativity is extensive but the mutual information is sub-extensive, indicating a large amount of undistillable, bound entanglement in thermalized states. For evaporating black holes at finite temperature, both the logarithmic negativity and the Petz map fidelity reveal an important new time scale tb, which is earlier than the Page time tp by a finite fraction of the total evaporation time. We find that tb, as opposed to tp, is the time scale at which quantum entanglement between different parts of the radiation becomes extensive, and the fidelity of information recovery for a large diary thrown into the black hole starts to grow.