Abstract Black-hole evaporation can be unitary only if Hawking's thermal spectrum is a coarse view of an underlying pure quantum process. Island and replica-wormhole calculations recover the Page curve but do not generally provide the amplitudes mapping a specified black-hole microstate to outgoing quanta. Here we construct such a state-resolved channel for an area-law quantum memory in matrix black-hole quantum mechanics. An exact symmetry separates the fermionic state into a geometric factor that controls emission and a protected factor untouched by the full real- and imaginary-time matrix and link dynamics. We prove that this memory occurs in every representation sector, enumerate all sectors through rank ten, and exhibit a self-complementary sector whose entropy scales with horizon area. When the matrix rank decreases, an exact branching isometry transfers the memory into daughter-hole and radiation degrees of freedom. Combining this isometry with the model's monopole-tunnelling weights gives every encoded state the same Hawking-thermal branch probabilities while its conditional radiation remains pure and microstate dependent. Finite-rank simulations show Page-like transfer and near-unit decoding; dephasing leaves the branch probabilities unchanged but erases recovery. The result provides an explicit amplitude-level mechanism by which Hawking thermality and unitary information transfer coexist in one microscopic model.
Abstract Black-hole evaporation can be unitary only if Hawking's thermal spectrum is a coarse view of an underlying pure quantum process. Island and replica-wormhole calculations recover the Page curve but do not generally provide the amplitudes mapping a specified black-hole microstate to outgoing quanta. Here we construct such a state-resolved channel for an area-law quantum memory in matrix black-hole quantum mechanics. An exact symmetry separates the fermionic state into a geometric factor that controls emission and a protected factor untouched by the full real- and imaginary-time matrix and link dynamics. We prove that this memory occurs in every representation sector, enumerate all sectors through rank ten, and exhibit a self-complementary sector whose entropy scales with horizon area. When the matrix rank decreases, an exact branching isometry transfers the memory into daughter-hole and radiation degrees of freedom. Combining this isometry with the model's monopole-tunnelling weights gives every encoded state the same Hawking-thermal branch probabilities while its conditional radiation remains pure and microstate dependent. Finite-rank simulations show Page-like transfer and near-unit decoding; dephasing leaves the branch probabilities unchanged but erases recovery. The result provides an explicit amplitude-level mechanism by which Hawking thermality and unitary information transfer coexist in one microscopic model.
We present a minimal, fully unitary toy model of black hole evaporation in which information recovery emerges from non-factorized global states and observer-dependent access. The model reproduces a Page-like entropy curve for Hawking radiation without invoking fundamental information loss, horizon microstructure, or spacetime geometry at the microscopic level. The result supports the interpretation that the black hole information paradox arises from regime-dependent coarse-graining rather than from a breakdown of quantum unitarity.
Abstract While recent progress in the black hole information problem has shown that the entropy of Hawking radiation follows a unitary Page curve, the quantum state of Hawking radiation prior the Page time is still treated as purely thermal, containing no information about the microstructure of the black hole. We demonstrate that there is significant quantum information regarding the quantum state of the black hole in the Hawking radiation prior to the Page time. By computing of the quantum fidelity in a 2D boundary conformal field theory (BCFT) model of black hole evaporation, we demonstrate that an observer outside of an evaporating black hole may distinguish different black holes via measurements of the Hawking radiation at any time during the evaporation process, albeit with an exponentially large number of measurements. Furthermore, our results are universal, applicable to general BCFTs including those with large central charge and rational BCFTs. The techniques we develop for computing the fidelity are more generally applicable to excited states in CFT. As such, we are able to characterize more general aspects of thermalization in 2D conformal field theory.
Gap G6 of the PTRH/TMRB framework called for proof that information encoded in the event-horizon-state computer memory (EHSCM, Paper 11) can be retrieved before the Page time lambda_Page, at which the Hawking radiation entropy equals the residual black-hole entropy. We provide three results at status [V] and one retrieval protocol. (i) Unconditional sector-label retrieval: the sector population distribution {p_n} is an exact conserved charge of the GKSL dynamics (Papers 16, 19) and is recoverable at any time from the instantaneous relative Hawking emission rates Gamma_n(lambda)/gamma(lambda) = p_n; no Page-time condition applies. (ii) Pre-Page within-sector capacity: the within-sector information capacity I_within(lambda) = S_BH(lambda) - H({p_n}) satisfies I_within(lambda) > S_BH(0)/2 - ln 9 > 0 for all lambda < lambda_Page, confirming that the horizon retains positive within-sector capacity throughout the pre-Page regime. (iii) Horizon-direct retrieval channel: the EHSCM ERASE operation implements a unitary extraction of the within-sector state rho_n(lambda) from H_n(lambda) into an output register with unit fidelity, independent of lambda. Since this channel operates directly on H(lambda) --- not on the Hawking radiation --- it is not subject to the Page-time limit on passive radiation decoding. The combination of (i) and (iii) yields a concrete pre-Page retrieval protocol with unit fidelity. Gap G6 is upgraded from [O] to [V]. Eight of nine PTRH gaps (G1, G2, G3, G4, G5, G6, G8, G9) now carry status [V]; one remains open (G7).
We formulate quantum evolution on growing causal domains as a family of quantum channels between generally non-isomorphic state spaces. Unitarity is replaced locally by approximate isometric evolution, measured with an energy-constrained diamond norm, while observer covariance is imposed through consistency, refinement, and cocycle conditions on causal overlaps. Applied to an evaporating black hole, the formalism yields a discrete isometric model in which information is transferred from the black-hole sector to the radiation sector without requiring a fixed global Hilbert-space factorization. A random-isometry approximation reproduces the Page transition and shows that a dynamically populated complementary sector produces a calculable endpoint defect in the Page curve. Information--disturbance bounds further imply that exact exterior unitarity forces the complementary channel to be input independent, while approximate unitarity quantitatively bounds structural leakage. The resulting framework interprets unitarity as an emergent property of observer-consistent causal descriptions rather than as a fundamental identification of state spaces at different times.
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.
This paper presents a structural resolution of the black-hole information-loss contradiction using standard quantum-information and operator-algebraic ideas. The central argument is that local horizon regularity, unitary evolution, locally thermal-looking radiation, no cloning, and complete final information recovery are not mutually inconsistent unless one additionally assumes that the interior partner and the radiation reconstruction must remain permanently independent physical subsystems. The paper develops an alternative framework in which globally encoded quantum information can remain invisible to the local horizon observable algebra while being preserved exactly in the total quantum state and progressively transferred into correlations within the emitted radiation. An explicit finite-dimensional code model demonstrates that each individual emitted subsystem can appear locally universal while arbitrary quantum information, including entanglement with an external reference system, remains exactly preserved and fully recoverable from the final radiation. The analysis also distinguishes the local horizon-partner role from the global microstate information and from the physical carrier that realizes either role at a given stage of evaporation. This separation removes the apparent monogamy conflict without violating linearity, no cloning, or unitary quantum mechanics. A complementary entropy analysis shows how a Page-like transition can arise when the responsibility for purification becomes progressively reconstructible from the radiation. The paper does not claim a complete dynamical theory of astrophysical black-hole evaporation. Instead, it establishes a mathematically explicit consistency framework showing that the standard information-loss contradiction is not forced by local thermality and unitarity alone, and it identifies the remaining physical problem as the derivation of the appropriate horizon observable algebra and evaporation dynamics from a complete theory of gravity.