Information Scrambling over Bipartitions: Equilibration, Entropy Production, and Typicality

Georgios Styliaris, Namit Anand, and Paolo Zanardi

Phys. Rev. Lett. 126, 030601 – Published 20 January 2021

Abstract

In recent years, the out-of-time-order correlator (OTOC) has emerged as a diagnostic tool for information scrambling in quantum many-body systems. Here, we present exact analytical results for the OTOC for a typical pair of random local operators supported over two regions of a bipartition. Quite remarkably, we show that this “bipartite OTOC” is equal to the operator entanglement of the evolution, and we determine its interplay with entangling power. Furthermore, we compute long-time averages of the OTOC and reveal their connection with eigenstate entanglement. For Hamiltonian systems, we uncover a hierarchy of constraints over the structure of the spectrum and elucidate how this affects the equilibration value of the OTOC. Finally, we provide operational significance to this bipartite OTOC by unraveling intimate connections with average entropy production and scrambling of information at the level of quantum channels.

Received 29 July 2020
Revised 2 December 2020
Accepted 7 December 2020

DOI:https://doi.org/10.1103/PhysRevLett.126.030601

Physics Subject Headings (PhySH)

Open quantum systems & decoherence Quantum chaos Quantum correlations in quantum information Quantum entanglement Quantum thermodynamics

Quantum chaotic systems

Many-body techniques

Quantum Information, Science & TechnologyGeneral PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Georgios Styliaris ^1,2,3, Namit Anand³, and Paolo Zanardi³

¹Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany
²Munich Center for Quantum Science and Technology, Schellingstrasse 4, 80799 München, Germany
³Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089, USA