QUANTUM INFORMATION SCRAMBLING AND PROTECTION IN MANY-BODY SYSTEM

Abstract

This work is focused on two main topics in quantum information theory: the scramblingof quantum information and the preservation of quantum information in many-body system. In terms of information scrambling, the main focus of this work is on the Out-of-time-order corre- lator (OTOC), which is used to probe the dynamics of quantum information as it spreads from localized degrees of freedom to those that are distributed throughout the system. On the other hand, the aim of the study of quantum information protection is to construct a system that can preserve quantum information for a sufficiently long time when coupled to a finite-temperature environment. The many-body systems analyzed in this work belong or are related to a class of stronglyinteracting systems known as holographic quantum models. The standard examples in this class are believed to be equivalent to gravitational theory in spacetime that is one-dimensional higher than that the quantum model lives in. Therefore, the results may also provide insights into topics in quantum gravity. The first part of the thesis explores the scrambling dynamics close to a critical point whereconformal symmetry emerges. The second case deals with the scrambling dynamics with con- servation law constraints in holographic quantum field theory. The result also clarifies how con- served charges influence the dynamics in the bulk dual. The third part of the thesis presents a matrix model with a large matrix rank N that belongs to the class of approximate quantum error correction codes. We investigate its thermal stability by coupling it to a thermal bath and demonstrate that it behaves as a self-correcting quantum memory at finite temperature. The coherent memory time scales polynomially with the system size N.