Order parameter for chaos

          @misc{ pirsa_15080069,
            doi = {10.48660/15080069},
            url = {https://pirsa.org/15080069},
            author = {Yoshida, Beni},
            keywords = {Quantum Fields and Strings, Quantum Gravity, Quantum Information},
            language = {en},
            title = {Order parameter for chaos },
            publisher = {Perimeter Institute},
            year = {2015},
            month = {aug},
            note = {PIRSA:15080069 see, \url{https://pirsa.org}}
          }
          

Abstract

The fact that a black hole is a fast-scrambler is at the heart of black hole information paradoxes. It has been suggested that chaos can be diagnosed by using an out-of-time correlation function, which is closely related to the commutator of operators separated in time. In this talk I propose that the tripartite information (also known as topological entanglement entropy) can be used as a quantitative information theoretic measure of chaos. By viewing a quantum channel as a state via the Choi-Jamilkowski isomorphism, the tripartite information measures four-party entanglement between the “past” and the “future”, much like an out-of-time correlation function. I will compute the time-evolution of the tripartite information for three systems; (a) non-integrable spin systems on a lattice, (b) planar networks of perfect tensors which mimic the growth of the Einstein-Rosen bridge and (c) a holographic system. This talk is based on an ongoing work with Xiaoliang Qi and Daniel Roberts.