Title: Introduction to Stationary and Ergodic Quantum Processes and their asymptotic behavior.
Abstract: In this talk, I will introduce the notion of a stationary and ergodic quantum process. These were initially introduced by Movassagh and Schenker in 2019, where they obtain an ergodic theorem for such processes. Under irreducibility and mixing conditions, we will further discuss the asymptotic behavior of such processes. We will obtain a law of large numbers and a central limit theorem involving the top (maximal) Lyapunov exponent. In the continuous-time parameter, a quantum process is represented by a double-indexed family of positive map-valued random variables. For a stationary and ergodic family of such maps, we extend the results by Movassagh and Schenker to the continuous case.
