Black holes as mirrors: quantum information in random subsystems Patrick Hayden and John Preskill Abstract: We study information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the “half-way” point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum error-correcting codes that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole’s information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementarity hypothesis. Keywords: Random Systems, Black Holes. The paper discusses the retrieval of quantum information from evaporating black holes. It assumes that black holes process quantum information rather than destroy it and applies insights from quantum information theory to study the information content of the Hawking radiation. The conclusion is that, under plausible dynamical assumptions, the black hole releases information remarkably quickly, much faster than might have been naively expected. The analysis has two main components. First, it assumes that a black hole thermalizes quantum information arbitrarily quickly, so that the internal dynamics of a black hole can be modeled by an instantaneous random unitary transformation. Under this assumption, it is shown that if a black hole's internal degrees of freedom are nearly maximally entangled with the previously emitted Hawking radiation, then k qubits of quantum information dumped into the black hole will be revealed after just a few more than k qubits are emitted in the Hawking radiation. Then, the issue of a black hole's thermalization time is reexamined, and it is argued that a black hole's internal quantum state becomes thoroughly mixed in a (Schwarzschild) time of order $ r_{S}\log(r_{S}/l_{P}) $, where $ r_{S} $ is the black hole's Schwarzschild radius and $ l_{P} $ is the Planck length. This argument relies on a recent construction of efficient quantum circuits that realize approximate unitary 2-designs. Combining with the preceding result, it is inferred that, for a black hole whose evaporation is past the half-way point, k qubits absorbed by the black hole will be reemitted in Schwarzschild time $ O(kr_{S}) $ or $ O(r_{S}\log(r_{S}/l_{P})) $, whichever is larger. The paper also addresses whether the claim that information escapes rapidly from black holes can be reconciled with the hypothesis of “black hole complementarity,” according to whichBlack holes as mirrors: quantum information in random subsystems Patrick Hayden and John Preskill Abstract: We study information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the “half-way” point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum error-correcting codes that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole’s information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementarity hypothesis. Keywords: Random Systems, Black Holes. The paper discusses the retrieval of quantum information from evaporating black holes. It assumes that black holes process quantum information rather than destroy it and applies insights from quantum information theory to study the information content of the Hawking radiation. The conclusion is that, under plausible dynamical assumptions, the black hole releases information remarkably quickly, much faster than might have been naively expected. The analysis has two main components. First, it assumes that a black hole thermalizes quantum information arbitrarily quickly, so that the internal dynamics of a black hole can be modeled by an instantaneous random unitary transformation. Under this assumption, it is shown that if a black hole's internal degrees of freedom are nearly maximally entangled with the previously emitted Hawking radiation, then k qubits of quantum information dumped into the black hole will be revealed after just a few more than k qubits are emitted in the Hawking radiation. Then, the issue of a black hole's thermalization time is reexamined, and it is argued that a black hole's internal quantum state becomes thoroughly mixed in a (Schwarzschild) time of order $ r_{S}\log(r_{S}/l_{P}) $, where $ r_{S} $ is the black hole's Schwarzschild radius and $ l_{P} $ is the Planck length. This argument relies on a recent construction of efficient quantum circuits that realize approximate unitary 2-designs. Combining with the preceding result, it is inferred that, for a black hole whose evaporation is past the half-way point, k qubits absorbed by the black hole will be reemitted in Schwarzschild time $ O(kr_{S}) $ or $ O(r_{S}\log(r_{S}/l_{P})) $, whichever is larger. The paper also addresses whether the claim that information escapes rapidly from black holes can be reconciled with the hypothesis of “black hole complementarity,” according to which