Ergodic and mixing quantum channels in finite dimensions

D. Burgarth, G. Chiribella, V. Giovannetti, P. Perinotti, K. Yuasa

Research output: Contribution to journalArticle

28 Citations (Scopus)

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.

Original languageEnglish
Article number073045
JournalNew Journal of Physics
Volume15
DOIs
Publication statusPublished - 2013 Jul 1

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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