Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics

Michael A. Rampp; Pieter W. Claeys

doi:10.22331/q-2024-08-08-1434

Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics

Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany

Published:	2024-08-08, volume 8, page 1434
Eprint:	arXiv:2312.03838v4
Doi:	https://doi.org/10.22331/q-2024-08-08-1434
Citation:	Quantum 8, 1434 (2024).

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Abstract

The Hayden-Preskill protocol probes the capability of information recovery from local subsystems after unitary dynamics. As such it resolves the capability of quantum many-body systems to dynamically implement a quantum error-correcting code. The transition to coding behavior has been mostly discussed using effective approaches, such as entanglement membrane theory. Here, we present exact results on the use of Hayden-Preskill recovery as a dynamical probe of scrambling in local quantum many-body systems. We investigate certain classes of unitary circuit models, both structured Floquet (dual-unitary) and Haar-random circuits. We discuss different dynamical signatures corresponding to information transport or scrambling, respectively, that go beyond effective approaches. Surprisingly, certain chaotic circuits transport information with perfect fidelity. In integrable dual-unitary circuits, we relate the information transmission to the propagation and scattering of quasiparticles. Using numerical and analytical insights, we argue that the qualitative features of information recovery extend away from these solvable points. Our results suggest that information recovery protocols can serve to distinguish chaotic and integrable behavior, and that they are sensitive to characteristic dynamical features, such as long-lived quasiparticles or dual-unitarity.

Featured image: Schematic representation of the Hayden-Preskill information recovery protocol. One party (Alice) inputs one half of a maximally entangled state (system A) into a black hole. Bob has established maximal entanglement with the initial state of the black hole (system B). If perfect recovery is possible, Bob can apply a unitary transformation to the emitted Hawking radition (D) and the entangled partner of the black-hole's initial state to establish maximal entanglement with Alice's state.

Popular summary

Almost twenty years ago, Hayden and Preskill introduced a simple thought experiment to shed light on the “black hole information paradox”. This apparent paradox stems from the observation that black holes only emit so-called Hawking radiation, black-body radiation that does not contain any information beyond its temperature. It seems that the information about objects that have fallen into the black hole has been lost! This destruction of information is at odds with the principles of quantum mechanics, and many scientists believe that black holes should ultimately be described quantum mechanically.

Hayden and Preskill modeled the black hole as a complicated quantum system of many degrees of freedom (a random unitary operator) and showed that the apparent paradox can be resolved by noticing that the quantum system distributes the information non-locally over many degrees of freedom such that it cannot be revealed by locally probing the emitted radiation.

They then argued that an observer that previously established entanglement with the black hole would be able to quickly recover any information thrown into the black hole.

In this paper – while we do not attempt to study black holes – we investigate how this process comes about in systems with local interactions, so-called unitary circuits, which are minimal models of quantum many-body systems that may be simulated on quantum computers. In particular, we are able to show that Hayden and Preskill’s prediction holds in certain exactly solvable models, namely in dual-unitary circuits. These circuits also showcase some unexpected behavior: They transport information perfectly over infinite distances despite being chaotic. Finally, we study if the Hayden-Preskill protocol is able to distinguish chaotic from regular (integrable) evolution. While we see that for small system sizes integrable systems scramble information much more slowly than chaotic ones, more work is needed to ascertain the behavior for very large systems.

► BibTeX data

@article{Rampp2024haydenpreskill,
  doi = {10.22331/q-2024-08-08-1434},
  url = {https://doi.org/10.22331/q-2024-08-08-1434},
  title = {Hayden-{P}reskill recovery in chaotic and integrable unitary circuit dynamics},
  author = {Rampp, Michael A. and Claeys, Pieter W.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1434},
  month = aug,
  year = {2024}
}

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