Invariance of Stationary and Ergodic Properties of a Quantum Source   under Memoryless Transformations
  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 ${\cal E}^{\otimes m}$, where a copy of ${\cal E}$ acts locally on each spin lattice site. We also establish ergodicity criteria for so called classically-correlated quantum sources. 
Alexei Kaltchenko and En-Hui Yang (University of Waterloo, Canada)