Ergodic and mixing quantum channels in finite dimensions

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

    Research output: Contribution to journalArticle

    25 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

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    ASJC Scopus subject areas

    • Physics and Astronomy(all)

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    Ergodic and mixing quantum channels in finite dimensions. / Burgarth, D.; Chiribella, G.; Giovannetti, V.; Perinotti, P.; Yuasa, Kazuya.

    In: New Journal of Physics, Vol. 15, 073045, 07.2013.

    Research output: Contribution to journalArticle

    Burgarth, D. ; Chiribella, G. ; Giovannetti, V. ; Perinotti, P. ; Yuasa, Kazuya. / Ergodic and mixing quantum channels in finite dimensions. In: New Journal of Physics. 2013 ; Vol. 15.
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