Probing the Spatial Distribution of Entanglement in Many-Body Quantum Systems

Entanglement is the most unique and distinguishing feature of quantum mechanics, and is of fundamental importance not only to the theory of quantum information, but to the study of quantum phases of matter. While much work has been done to study the entanglement in the ground states of familiar systems like conformal field theories and gapped topological phases, slightly less attention has been paid to dynamical quantum systems and systems that lack translational invariance. In this thesis, I will first introduce some basic formalism and intuition related to entanglement in many-body quantum systems. I will then discuss an elegant means of calculating entanglement entropy and other measures in conformal field theories on curved backgrounds via the Ryu/Takyanagi formula. Next, I will introduce a general formula for the calculation of the entanglement contour, a well-behaved entanglement density function. We will show the contour to be particularly useful for probing the dynamics of out-of-equilibrium quantum systems. With these dynamical systems in mind, I will present results from calculations of multipartite operator entanglement — a state-independent entanglement measure — in a many-body localized system. Finally, I will conclude with a description of a new method to simulate two dimensional tensor network states on a quantum computer, as a means of realizing entangled quantum matter in a controlled, experimental setting. I also include results from an experimental proof-of-concept of this method.