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Information Scrambling over Bipartitions: Equilibration, Entropy Production, and Typicality
Georgios Styliaris1,2,3, Namit Anand3, Paolo Zanardi3
1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany.
Physical Review Letters
|February 5, 2021
Summary
We introduce the bipartite out-of-time-order correlator (OTOC) for quantum systems. This novel measure reveals deep connections between operator entanglement, spectral properties, and information scrambling in many-body dynamics.
Area of Science:
- Quantum Information Theory
- Condensed Matter Physics
- Quantum Many-Body Systems
Background:
- The out-of-time-order correlator (OTOC) is a key observable for diagnosing information scrambling.
- Understanding information scrambling is crucial for characterizing quantum chaos and thermalization.
- Previous studies focused on OTOCs for specific systems, limiting general insights.
Purpose of the Study:
- To introduce and analyze a
- bipartite OTOC
- for general quantum many-body systems.
- To establish analytical results connecting the bipartite OTOC with operator entanglement and entangling power.
- To explore the relationship between long-time OTOC averages, eigenstate entanglement, and spectral properties.
Main Methods:
- Exact analytical calculations of the bipartite OTOC for random local operators.
- Analysis of the interplay between bipartite OTOC, operator entanglement, and entangling power.
- Computation of long-time averages of the OTOC and their connection to eigenstate entanglement.
- Investigation of spectral constraints in Hamiltonian systems and their effect on OTOC equilibration.
Main Results:
- The bipartite OTOC is shown to be equal to the operator entanglement of the evolution.
- The interplay between bipartite OTOC and entangling power is precisely determined.
- Long-time averages of the OTOC are linked to eigenstate entanglement.
- A hierarchy of spectral constraints is uncovered for Hamiltonian systems, influencing OTOC equilibration.
- The bipartite OTOC demonstrates operational significance through connections with entropy production and quantum channel information scrambling.
Conclusions:
- The bipartite OTOC provides a powerful new tool for quantifying information scrambling.
- It establishes a direct link between operator entanglement and scrambling dynamics.
- The study reveals fundamental connections between spectral properties, entanglement, and thermalization in quantum systems.
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