Entropy in Quantum Information Theory and Condensed Matter Physics Matthew Hastings, Senior Research Scientist, Microsoft Research, Station Q, Santa Barbara

While entropy was introduced in thermodynamics to describe heat engines, its applications have spread to widely different areas. I will talk about recent research on two such problems. The first is a problem in information theory: how much information can we send over a noisy communication channel, given that the world is described by quantum mechanics? I will explain the so-called "additivity conjecture", which was a proposed way to calculate the communication capacity of such a channel, and I will explain my recent result disproving this conjecture, showing that we can use entanglement to boost communication capacity. The second problem is in quantum systems far from equilbrium. Here I will describe how entropy can arise from quantum entanglement, and I will discuss novel simulation algorithms and future experiments probing the relaxation back to local thermal equilibrium.