The Quantum Mechanics of Rare Events

Determining the tail of probability distributions is an important topic in many physical settings. For classical stochastic systems, much about these processes has been understood using the large deviation principle. Much less is known in quantum systems, especially with many degrees of freedom (such as in quantum field theory). Inspired by applications to cosmology, I will discuss rare fluctuations in quantum walks and their origins in terms of entropies. I will discuss implications for several examples including eternal inflation and quantum fisher information.