Quantum Predictor Models

We define a class of finitely parameterizable stochastic models, Quantum Predictor Models (QPMs), such that, in an obvious manner, a collection of prevalent quantum statistical phenomena can be described by their means. Moreover, we identify the induced class of discrete random processes with the class of finite-dimensional processes, which enjoy nice ergodic properties and a graphical representation. For the subclass of Quantum Markov Chains (QMCs), which reflect most of the real-world quantum processes, we can give an even stronger version of the ergodic theorem available for general QPMs, thereby also strengthening an ergodic theorem, which has recently been proved for the class of Quantum Walks on Graphs.