Perron-Frobenius Theory of Ergodic Quantum Processes

Matthew Lagro, Wei-Shih Yang, Sheng Xiong

Abdessatar Souissi

Owen Ekblad, Jeffrey Schenker

We study the periodic properties of sequences of quantum channels sampled from an ergodic stochastic process satisfying a natural irreducibility condition. We relate these periodic properties to certain global spectral data defined by the sequence of quantum channels, proving a general Perron-Frobenius-type theorem that in particular constitutes a full generalization of the work of Evans and Høegh-Krohn to the disordered setting.

Ramis Movassagh, Jeffrey Schenker

Owen Ekblad, Jeffrey Schenker

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.

Yu. N. Barabanenkov, Vladimir D. Ozrin, A. V. Shelest