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

Understand

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.