One of the most fun arXiv preprints I’ve read in a while:
Black holes as mirrors: quantum information in random subsystems
by 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.
Many of this paper’s arguments depend on speculative assumptions about quantum gravity, and might very well be wrong. What’s nice is simply that they’re not not even wrong! This is an 18-page paper about the Planck-scale dynamics of black hole horizons where I never once found myself wondering what the authors were trying to say, or how their ideas would in principle be tested.
When I used to spout off about the complexity of retrieving information from a black hole as a function of the Schwarzschild radius rS, people assumed I was just fishing for laughs. And they were basically right. But even then, I felt sure that actual physicists would eventually say something real about this question, unapologetically using the language of quantum computing and information. Like Alice with her k qubits, I didn’t have to wait as long as I’d thought.