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arXiv · 1210.5625

Ergodic and Mixing Quantum Channels in Finite Dimensions

Daniel Burgarth·Giulio Chiribella·Vittorio Giovannetti·Paolo Perinotti·Kazuya Yuasa
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Abstract

The paper provides a systematic characterization of quantum ergodic and mixing channels in finite dimensions and a discussion of their structural properties. In particular, we discuss ergodicity in the general case where the fixed point of the channel is not a full-rank (faithful) density matrix. Notably, we show that ergodicity is stable under randomizations, namely that every random mixture of an ergodic channel with a generic channel is still ergodic. In addition, we prove several conditions under which ergodicity can be promoted to the stronger property of mixing. Finally, exploiting a suitable correspondence between quantum channels and generators of quantum dynamical semigroups, we extend our results to the realm of continuous-time quantum evolutions, providing a characterization of ergodic Lindblad generators and showing that they are dense in the set of all possible generators.

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Daniel Burgarth, Giulio Chiribella, Vittorio Giovannetti, Paolo Perinotti, Kazuya Yuasa. 2013-08-05. Ergodic and Mixing Quantum Channels in Finite Dimensions. https://doi.org/10.1088/1367-2630%2F15%2F7%2F073045

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