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arXiv:2406.10982

Reducibility Theory and Ergodic Theorems for Ergodic Quantum Processes

Owen Ekblad, Jeffrey Schenker

Published Jun 16, 2024• 0 citations
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Abstract

We develop a Perron-Frobenius type theory for products of random quantum channels acting on finite-dimensional matrix algebras sampled from a stationary and ergodic stochastic process, which, in keeping with the literature, we call ergodic quantum processes. This serves as a unifying framework for many models, including i.i.d., Markovian, periodic, and quasiperiodic models. We establish various characterizations of irreducibility, from which we recover a number of general ergodic theorems. We then analyze some specific examples, and, in particular, give a refinement of our theory in the i.i.d. case.

DOI
10.48550/arxiv.2406.10982

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