PIRSA:18010084

Entanglement, quantum randomness, and complexity beyond scrambling

Liu, Z. (2018). Entanglement, quantum randomness, and complexity beyond scrambling . Perimeter Institute. https://pirsa.org/18010084

Liu, Zi-Wen. Entanglement, quantum randomness, and complexity beyond scrambling . Perimeter Institute, Jan. 24, 2018, https://pirsa.org/18010084 

          @misc{ pirsa_PIRSA:18010084,
            doi = {10.48660/18010084},
            url = {https://pirsa.org/18010084},
            author = {Liu, Zi-Wen},
            keywords = {Quantum Information},
            language = {en},
            title = {Entanglement, quantum randomness, and complexity beyond scrambling },
            publisher = {Perimeter Institute},
            year = {2018},
            month = {jan},
            note = {PIRSA:18010084 see, \url{https://pirsa.org}}
          }

Zi-Wen Liu Tsinghua University

DOI 10.48660/18010084
Collection
Talk Type Scientific Series
Subject

Abstract

The entanglement properties of random quantum states or dynamics are important to the study of a broad spectrum of disciplines of physics, ranging from quantum information to high energy and many-body physics. This work investigates the interplay between the degrees of entanglement and randomness in pure states and unitary channels, by employing tools from random matrix theory, representation theory, combinatorics, Weingarten calculus etc. We reveal strong connections between designs (distributions of states or unitaries that match certain moments of the uniform Haar measure) and generalized entropies (entropic functions that depend on certain powers of the density operator), by showing that Renyi entanglement entropies averaged over designs of the same order are almost maximal. This strengthens the celebrated Page's theorem. Moreover, we find that designs of an order that is logarithmic in the dimension maximize all Renyi entanglement entropies, and so are completely random in terms of the entanglement spectrum. Our results relate the behaviors of Renyi entanglement entropies to the complexity beyond scrambling/thermalization/chaos in terms of the degree of randomness, and suggest a generalization of the fast scrambling conjecture.  (Refs: 1703.08104, 1709.04313)