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

TL;DR

This paper analytically investigates the bipartite out-of-time-order correlator (OTOC) in quantum many-body systems, revealing its relation to operator entanglement, eigenstate entanglement, and entropy production, thus advancing understanding of information scrambling.

Contribution

It provides exact analytical results for the bipartite OTOC, linking it to operator entanglement, spectral constraints, and entropy production, offering new insights into quantum information scrambling.

Findings

Bipartite OTOC equals operator entanglement of evolution.

Long-time averages of OTOC relate to eigenstate entanglement.

Hierarchy of spectral constraints influences OTOC equilibration.

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.