The Generalized Lyapunov Theorem and its Application to Quantum Channels

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dc.creatorBurgarth, Daniel
dc.creatorGiovannetti, Vittorio
dc.date2006-05-23
dc.date2007-03-09
dc.date.accessioned2026-07-07T08:09:37Z
dc.date.available2026-07-07T08:09:37Z
dc.descriptionWe give a simple and physically intuitive necessary and sufficient condition for a map acting on a compact metric space to be mixing (i.e. infinitely many applications of the map transfer any input into a fixed convergency point). This is a generalization of the "Lyapunov direct method". First we prove this theorem in topological spaces and for arbitrary continuous maps. Finally we apply our theorem to maps which are relevant in Open Quantum Systems and Quantum Information, namely Quantum Channels. In this context we also discuss the relations between mixing and ergodicity (i.e. the property that there exist only a single input state which is left invariant by a single application of the map) showing that the two are equivalent when the invariant point of the ergodic map is pure.
dc.description13 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/quant-ph/0605197
dc.identifierhttp://arxiv.org/abs/quant-ph/0605197
dc.identifierNew J. Phys. 9 150 (2007)
dc.identifierdoi:10.1088/1367-2630/9/5/150
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/131593
dc.subjectQuantum Physics
dc.subjectMathematical Physics
dc.titleThe Generalized Lyapunov Theorem and its Application to Quantum Channels
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