QLunch: Lucas Hackl

Speaker: Lucas Hackl, University of Melbourne

Title: Volume-law entanglement entropy of typical pure quantum states


In this talk, I will discuss the statistical properties of the entanglement entropy, which serves as a natural measure of quantum correlations between a subsystem and its complement. Entanglement is a defining feature of quantum theory and understanding its statistical properties has applications in many areas of physics.
First, I will introduce the class of physical models and explain its relevance for practical applications. Second, I will explain how the statistical ensemble of quantum states can naturally be described through the methods of random matrix theory. Third and finally, I will discuss a number of new results describing the typical properties (e.g., average, variance) of the entanglement entropy for various ensembles of quantum states (general vs. Gaussian, arbitrary vs. fixed particle number). See arXiv:2103.05416 for further details.