期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2011
卷号：2011
DOI：10.1155/2011/740816
出版社：Hindawi Publishing Corporation
摘要：In a quantum Markov chain, the temporal succession of states
is modeled by the repeated action of a “bistochastic quantum operation” on
the density matrix of a quantum system. Based on this conceptual framework,
we derive some new results concerning the evolution of a quantum system,
including its long-term behavior. Among our findings is the fact that
the Cesàro limit of any quantum Markov chain always exists and equals
the orthogonal projection of the initial state upon the eigenspace of the
unit eigenvalue of the bistochastic quantum operation. Moreover, if the
unit eigenvalue is the only eigenvalue on the unit circle, then the quantum
Markov chain converges in the conventional sense to the said orthogonal
projection. As a corollary, we offer a new derivation of the classic result
describing limiting distributions of unitary quantum walks on finite graphs
(Aharonov et al., 2001).
