Invariance of Stationary and Ergodic Properties of a Quantum Source under Memoryless Transformations

Abstract

We prove that the stationarity and the ergodicity of a quantum source are preserved by any trace-preserving completely positive linear map of the tensor product form ${\mathcal{E}}^{\otimes m}$, where a copy of $\mathcal{E}$ acts locally on each spin lattice site. We also establish ergodicity criteria for so called classically-correlated quantum sources.

9 pages, no figures; typos corrected, appendix and references added