The free mutual information as a measure of quantum chaos

          @misc{ scivideos_PIRSA:25060012,
            doi = {10.48660/25060012},
            url = {https://pirsa.org/25060012},
            author = {Vardhan, Shreya},
            keywords = {Quantum Gravity, Quantum Information},
            language = {en},
            title = {The free mutual information as a measure of quantum chaos},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2025},
            month = {jun},
            note = {PIRSA:25060012 see, \url{https://scivideos.org/index.php/pirsa/25060012}}
          }
          

Abstract

I will introduce a quantity from noncommutative probability theory called the free mutual information, and discuss how it can be used as a new diagnostic of quantum many-body chaos. This quantity captures a notion of the spreading of the operator in the abstract space of all possible time-evolved operators, rather than the more familiar notion of spreading in the physical space of degrees of freedom. I will discuss a precise relation between the free mutual information and the higher-point out-of-time-ordered correlators which applies in any system. I will further discuss the behaviour of the free mutual information in a few representative models of chaotic systems, and how it is sensitive to features of the dynamics beyond those captured by the four-point out-of-time-ordered correlator.