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.
|Titolo:||Ergodic and mixing quantum channels in finite dimensions|
|Data di pubblicazione:||2013|
|Parole Chiave:||POSITIVE MAPS; INFORMATION-THEORY; ALGEBRAS; DYNAMICS; THEOREM; STATES|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1088/1367-2630/15/7/073045|
|Appare nelle tipologie:||1.1 Articolo in rivista|