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On Limiting Distributions of Quantum Markov Chains
Joint Authors
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-08-25
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
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).
American Psychological Association (APA)
Liu, Chaobin& Petulante, Nelson. 2011. On Limiting Distributions of Quantum Markov Chains. International Journal of Mathematics and Mathematical Sciences،Vol. 2011, no. 2011, pp.1-12.
https://search.emarefa.net/detail/BIM-494971
Modern Language Association (MLA)
Liu, Chaobin& Petulante, Nelson. On Limiting Distributions of Quantum Markov Chains. International Journal of Mathematics and Mathematical Sciences No. 2011 (2011), pp.1-12.
https://search.emarefa.net/detail/BIM-494971
American Medical Association (AMA)
Liu, Chaobin& Petulante, Nelson. On Limiting Distributions of Quantum Markov Chains. International Journal of Mathematics and Mathematical Sciences. 2011. Vol. 2011, no. 2011, pp.1-12.
https://search.emarefa.net/detail/BIM-494971
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-494971