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Law of large numbers and central limit theorem for ergodic quantum processes. (arXiv:2303.08992v1 [math-ph])

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A discrete quantum process is represented by a sequence of quantum
operations, which are completely positive maps that are not necessarily trace
preserving. We consider quantum processes that are obtained by repeated
iterations of a quantum operation with noise. Such ergodic quantum processes
generalize independent quantum processes. An ergodic theorem describing
convergence to equilibrium for a general class of such processes was recently
obtained by Movassagh and Schenker. Under irreducibility and mixing conditions,
we obtain a central limit type theorem describing fluctuations around the
ergodic limit.

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