QLunch: Lubashan Pathirana

Speaker: Lubashan Pathirana

Title: Introduction to Stationary (and Ergodic) Quantum Processes and their limiting behavior.

Abstract: Given a sequence of random quantum operations (completely positive super-operators that are not necessarily trace preserving) a random quantum process is obtained by iterated compositions. We study the case where the sequence is strictly stationary or ergodic, both instances being a generalization of the IID case. Under certain irreducibility assumptions we shall discuss the limiting behavior of such iterated compositions using techniques that comes from the study of products of random matrices. Like the case of products of random matrices, we see that the asymptotics of such iterated compositions are governed by the top (maximal) Lyapunov exponent. For the ergodic case we obtain a Law of Large numbers and under mixing conditions we obtain a Central Limit type theorem. If time permits, I will also introduce the notion of a continuous parameter quantum process and talk about their limiting behavior.