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Springer Series in Astrophysics and Cosmology

Information Scrambling at Quantum Hall Interfaces and Their Analog to Black Hole Event Horizon

Ken K. W., Kun Yang

Published Jan 1, 2025• 0 citations
Publisher
DOI
10.1007/978-981-96-6170-1_21

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Information Scrambling at Quantum Hall Interfaces and Their Analog to Black Hole Event Horizon

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The black hole information paradox has been hotly debated for the last few decades without a full resolution. This makes it desirable to find analogues of this paradox in simple and experimentally accessible systems, whose resolutions may shed light on this longstanding and fundamental problem. Here, we review and resolve the apparent "information paradox" in two different interfaces separating Abelian and non-Abelian quantum Hall states. In both cases, the information carried by the pseudospin degree of freedom of the Abelian anyons get scrambled when they cross the interface and enter the non-Abelian quantum Hall liquid. Nevertheless, it is found that the scrambling mechanism depends on the nature of the interface. The corresponding analogues of different concepts in black hole physics such as event horizon, black hole interior, Hawking radiation, and Page curve will also be discussed.

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This preprint provides a self-contained pedagogical introduction to black hole information scrambling and quantum chaos, aimed at advanced undergraduates and beginning graduate students. It covers the derivation of Hawking temperature and Bekenstein–Hawking entropy, the gravitational butterfly effect, the Lyapunov exponent, and the saturation of the universal quantum chaos bound by black holes. Numerical estimates across eight decades of black hole mass are presented, including a verification of the universal invariant λL · t∗ = ln S. The manuscript develops an explicit analogy between black hole scrambling and all-to-all random quantum circuits, making connections to quantum information theory tangible. Three worked problems suitable for classroom or self-study use are included. Keywords: black holes, quantum chaos, information scrambling, Lyapunov exponent, fast scramblers, random quantum circuits, Sachdev–Ye–Kitaev model, pedagogical preprint Notes: Preprint; Python code reproducing results is available at https://github.com/muhnehh/blackhole-scrambling.

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A possible solution of the information paradox can be sought in quantum information scrambling. In this paradigm, it is postulated that all information entering a black hole is rapidly and chaotically distributed across the event horizon, making it impossible to reconstruct the information by means of any local measurement. However, in this scenario, the effects of decoherence are typically ignored, which may render information scrambling moot in cosmological settings. In this work, we develop key steps toward a thermodynamic description of information scrambling in open quantum systems. In particular, we separate the entropy change into contributions arising from scrambling and decoherence, for which we derive statements of the second law. This is complemented with a numerical study of the SachdevYe-Kitaev, Maldacena-Qi, XXX, mixed-field Ising, and Lipkin-Meshkov-Glick models in the presence of decoherence in the energy or in the computational basis.

•Aug 12, 2020•44 citations
The black hole information paradox has been hotly debated for the last few decades without a full resolution. This makes it desirable to find analogues of this paradox in simple and experimentally accessible systems, whose resolutions may shed light on this longstanding and fundamental problem. Here, we review and resolve the apparent "information paradox" in two different interfaces separating Abelian and non-Abelian quantum Hall states. In both cases, the information carried by the pseudospin degree of freedom of the Abelian anyons get scrambled when they cross the interface and enter the non-Abelian quantum Hall liquid. Nevertheless, it is found that the scrambling mechanism depends on the nature of the interface. The corresponding analogues of different concepts in black hole physics such as event horizon, black hole interior, Hawking radiation, and Page curve will also be discussed.
This preprint provides a self-contained pedagogical introduction to black hole information scrambling and quantum chaos, aimed at advanced undergraduates and beginning graduate students. It covers the derivation of Hawking temperature and Bekenstein–Hawking entropy, the gravitational butterfly effect, the Lyapunov exponent, and the saturation of the universal quantum chaos bound by black holes. Numerical estimates across eight decades of black hole mass are presented, including a verification of the universal invariant λL · t∗ = ln S. The manuscript develops an explicit analogy between black hole scrambling and all-to-all random quantum circuits, making connections to quantum information theory tangible. Three worked problems suitable for classroom or self-study use are included. Keywords: black holes, quantum chaos, information scrambling, Lyapunov exponent, fast scramblers, random quantum circuits, Sachdev–Ye–Kitaev model, pedagogical preprint Notes: Preprint; Python code reproducing results is available at https://github.com/muhnehh/blackhole-scrambling.
A possible solution of the information paradox can be sought in quantum information scrambling. In this paradigm, it is postulated that all information entering a black hole is rapidly and chaotically distributed across the event horizon, making it impossible to reconstruct the information by means of any local measurement. However, in this scenario, the effects of decoherence are typically ignored, which may render information scrambling moot in cosmological settings. In this work, we develop key steps toward a thermodynamic description of information scrambling in open quantum systems. In particular, we separate the entropy change into contributions arising from scrambling and decoherence, for which we derive statements of the second law. This is complemented with a numerical study of the SachdevYe-Kitaev, Maldacena-Qi, XXX, mixed-field Ising, and Lipkin-Meshkov-Glick models in the presence of decoherence in the energy or in the computational basis.