Black holes as mirrors: Quantum information in random subsystems

By Patrick M. Hayden, John Preskill. 2007

1,488 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/5f96447e63d793db0699534da9b38548e9564f95

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. D. Harlow
2. D. Stanford
3. J. Maldacena
4. R. Myers
5. S. Raju
6. L. Susskind
7. S. Shenker
8. Zhenbin Yang

In Atomic and Molecular Physics, and Optics

1. A. Nahum
2. D. Harlow
3. D. Stanford
4. S. Raju
5. Brian Swingle
6. S. Shenker
7. L. Susskind
8. V. Khemani

In Nuclear and High Energy Physics

1. D. Stanford
2. D. Harlow
3. J. Maldacena
4. S. Raju
5. R. Myers
6. L. Susskind
7. S. Shenker
8. Zhenbin Yang

Citations in the corpus

• Scrambling Dynamics and Out-of-Time-Ordered Correlators in Quantum Many-Body Systems (2022, methodology): “[7] was: if another qubit is thrown into the black hole, then how long does one have to wait until the information in that qubit is available again in the subsequent radiation.”
• The Page curve of Hawking radiation from semiclassical geometry (2019, methodology): “Given the existence of these islands, it would be interesting to see whether there exists a method to extract the information contained within them that has a clear bulk interpretation, in the spirit of what was discussed for the Hayden-Preskill problem [48] in [49,50].”
• Dynamical Purification Phase Transition Induced by Quantum Measurements (2019, background): “The general argument was based on the idea of quantum information scrambling in chaotic systems applied to quantum error correction problems [71], which, at a technical level, is related to the decoupling property of two-designs such as (by definition) Haar random unitaries or the Clifford group [72”
• Random Quantum Circuits are Approximate 2-designs (2008, background): “[21] in that they consider nearest-neighbour interactions and we do not, our techniques and results could be readily extended to cover the case they consider.”
• Onset of many-body chaos in the $O(N)$ model (2017, background): “Scrambling is fundamentally an information theoretic notion [19,20], but the growth of scrambling can also be probed using special correlation functions as we discuss below [21,22].”
• Unitary designs from statistical mechanics in random quantum circuits. (2019, background): “From a quantum information perspective, random quantum circuits are low-depth constructions of unitary k -designs [1, 2], rapid information scramblers [3, 4], and essentially optimal decouplers [5].”
• Chaos and complexity by design (2016, methodology): “1 we reconsider the Hayden-Preskill notion of black hole scrambling [1].”
• Brownian Motion in AdS/CFT (2008, neutral): “This is reminiscent of the recent conjecture [41, 42] that black holes can scramble information very fast, whose dual picture is that a degree of freedom in the boundary theory interacts with a huge number of other degrees of freedom simultaneously.”
• Cool horizons for entangled black holes (2013, background): “se errors act in a simple way in the radiation basis, which we view as the computational basis. Because the radiation system is in a random state one expects the encoding of A 35 to be fault-tolerant [34]. This means that is it possible to correct the errors. One can correct errors which act on less”
• Second law of quantum complexity (2017, background): “(15) By a Hayden-Preskill circuit we mean a circuit of K qubits such that in each time step the qubits are paired and interact through K=2 gates [16].”
• On the dynamics of near-extremal black holes (2018, background): “J H E P 0 9 ( 2 0 1 8 ) 0 4 8 These developments are of considerable interest from the point of view of studying black hole dynamics, [28, 29].”
• Operator Spreading in Random Unitary Circuits (2017, background): “[16] Patrick Hayden and John Preskill, “Black holes as mirrors: quantum information in random subsystems,” Journal of High Energy Physics 2007, 120 (2007).”