Black holes as mirrors: quantum information in random subsystems

TL;DR

This paper argues that if black hole dynamics are unitary and rapidly mixing, the information entering a black hole is not destroyed but can be retrieved from Hawking radiation with remarkable speed. Using classical and quantum randomization models, it shows that after evaporation passes the halfway mark, information deposited in the black hole becomes accessible after only a small additional emission of qubits, and, in the quantum case, that k qubits can be recovered with fidelity via entanglement-assisted quantum communication. The authors connect these findings to the quantum erasure channel and propose efficient encoding via approximate unitary designs or local circuits, while discussing the decoding complexity and the no-cloning constraints that must be respected to preserve consistency with quantum mechanics. The work reframes the information paradox in terms of information-theoretic capacity and error-correcting codes, suggesting that black holes may encode and release quantum information much more rapidly than naïvely expected, albeit under stringent dynamical and computational assumptions.

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.

Figures (2)

• Figure 1: Information retrieval from an evaporating black hole. The black hole, which has been evaporating for a long time, has become maximally entangled with the previously emitted radiation system $E$. At this stage, the black hole swallows Alice's quantum memory $M$, which is maximally entangled with Charlie's reference system $N$. The internal dynamics of the black hole applies a strongly mixing unitary transformation $V^B$, and then the additional radiation system $R$ is emitted, where the dimension of $R$ is somewhat larger than the dimension of $M$. Now a subsystem of $RE$, controlled by Bob, is nearly maximally entangled with $N$ --- the content of Alice's quantum memory has escaped from the black hole and is in Bob's possession.
• Figure 2: Alice and Bob test whether an evaporating black hole clones quantum information. Alice, carrying her quantum memory, drops into the black hole. Bob recovers the content of Alice's memory from the Hawking radiation, and then enters the black hole, too. Alice sends her qubits to Bob, and Bob verifies that cloning has occurred.