Ergodic and mixing quantum channels in finite dimensions

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

53 Citations (SciVal)
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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.

Original languageEnglish
Article number073045
Number of pages33
JournalNew Journal of Physics
Volume15
DOIs
Publication statusPublished - 24 Jul 2013

Keywords

  • POSITIVE MAPS
  • INFORMATION-THEORY
  • ALGEBRAS
  • DYNAMICS
  • THEOREM
  • STATES

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