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Entropy
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Scrambling of Quantum Information in Chaotic Quantum Systems
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Scrambling of Quantum Information in Chaotic Quantum Systems

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: closed (31 July 2022) | Viewed by 3720

Special Issue Editors

Prof. Dr. Levan Chotorlishvili

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Guest Editor
Institut für Physik, Martin-Luther-Universität, Halle-Wittenberg, D-06099 Halle/Saale, Germany
Interests: spintronics and spin-caloritronics; KAM theory and quantum chaos; quantum information theory; ultra-high-energy neutrino physics; open quantum systems; quantum measurements
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Arthur Ernst

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Guest Editor
Institute for Theoretical Physics, Johannes Kepler University Linz, Altenberger Straße 69, 4040 Linz, ‬Austria
Interests: density functional theory; many-body physics; theoretical physics; computational physics

Special Issue Information

Dear Colleagues,

Nonlinear classical dynamical systems are predominantly chaotic, meaning that arbitrary small uncertainties in the initial conditions accumulate over an evolving period to the significant inaccuracy. When this happens, typically, dynamical description does not make sense and methods of statistical physics become necessary.

In contrast to the classical systems, in a quantum case, we do not have phase trajectories. Therefore, an alternative tool to test quantum chaos is in question. Larkin and Ovchinnikov introduced the concept of the out-of-time-ordered correlator (OTOC) of the operator, and since then, OTOC has been seen as a diagnostic tool of quantum chaos. Interest in the delocalization of quantum information (i.e., the scrambling of quantum entanglement) was renewed recently.

OTOC quantifies how swiftly quantum information initially encoded in terms of local operators spreads. The scrambling time is specified through the classical Lyapunov exponent. In essence, scrambling is a quantum version of the butterfly effect. During the last few years, OTOC became a hot spot in statistical physics. However, many questions still are not answered.

This Special Issue is a platform for discussion about problems related to the scrambling of quantum information in chaotic quantum systems.

Prof. Dr. Levan Chotorlishvili
Prof. Dr. Arthur Ernst
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • nonlinear resonance
  • random matrix theory
  • KAM theory
  • entanglement
  • OTOC
  • scrambling

Published Papers (1 paper)

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Research

20 pages, 608 KiB  
Article
Isospectral Twirling and Quantum Chaos
by Lorenzo Leone, Salvatore F. E. Oliviero and Alioscia Hamma
Entropy 2021, 23(8), 1073; https://0-doi-org.brum.beds.ac.uk/10.3390/e23081073 - 19 Aug 2021
Cited by 23 | Viewed by 2808
Abstract
We show that the most important measures of quantum chaos, such as frame potentials, scrambling, Loschmidt echo and out-of-time-order correlators (OTOCs), can be described by the unified framework of the isospectral twirling, namely the Haar average of a k-fold unitary channel. We [...] Read more.
We show that the most important measures of quantum chaos, such as frame potentials, scrambling, Loschmidt echo and out-of-time-order correlators (OTOCs), can be described by the unified framework of the isospectral twirling, namely the Haar average of a k-fold unitary channel. We show that such measures can then always be cast in the form of an expectation value of the isospectral twirling. In literature, quantum chaos is investigated sometimes through the spectrum and some other times through the eigenvectors of the Hamiltonian generating the dynamics. We show that thanks to this technique, we can interpolate smoothly between integrable Hamiltonians and quantum chaotic Hamiltonians. The isospectral twirling of Hamiltonians with eigenvector stabilizer states does not possess chaotic features, unlike those Hamiltonians whose eigenvectors are taken from the Haar measure. As an example, OTOCs obtained with Clifford resources decay to higher values compared with universal resources. By doping Hamiltonians with non-Clifford resources, we show a crossover in the OTOC behavior between a class of integrable models and quantum chaos. Moreover, exploiting random matrix theory, we show that these measures of quantum chaos clearly distinguish the finite time behavior of probes to quantum chaos corresponding to chaotic spectra given by the Gaussian Unitary Ensemble (GUE) from the integrable spectra given by Poisson distribution and the Gaussian Diagonal Ensemble (GDE). Full article
(This article belongs to the Special Issue Scrambling of Quantum Information in Chaotic Quantum Systems)
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