On the ergodic principle for Markov processes associated with quantum quadratic stochastic processes

In [1] the non-stationaryMarkov process generated by a quantum quadratic stochastic process (QQSP) was defined, and it was noted that if the QQSP satisfies the ergodic principle, then so does the Markov process. In the present article we use a decomposition of a QQSP (see [2]) to prove that the converse is also true, that is, if the Markov process satisfies the ergodic principle, then so does the corresponding QQSP.

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