A multiplicative ergodic theorem for disordered quantum processes

Repeated compositions of quantum channels arise naturally in many places across quantum: they arise, for example, in the transfer operator approach to quantum spin chains, and also in the repeated interactions description of open quantum dynamics. Assuming the system of interest is subject to some amount of disorder, it is therefore natural that one consider repeated compositions of random quantum channels, i.e., quantum channels sampled from a stochastic process. Under a stationarity assumption, such compositions fit well into the mathematical framework of Oseledets’s classical Multiplicative Ergodic Theorem (MET); in this talk, I shall discuss my recent work refining the MET for repeated compositions of random bistochastic quantum channels, and, time-permitting, I shall describe applications of this work to understanding entanglement breaking properties of such compositions.