Asymptotic Properties of Quantum Markov Chains

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F12%3A00199212" target="_blank" >RIV/68407700:21340/12:00199212 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1088/1751-8113/45/48/485301" target="_blank" >http://dx.doi.org/10.1088/1751-8113/45/48/485301</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1751-8113/45/48/485301" target="_blank" >10.1088/1751-8113/45/48/485301</a>

Result language
angličtina
Original language name
Asymptotic Properties of Quantum Markov Chains
Original language description
The asymptotic dynamics of discrete quantum Markov chains generated by the most general physically relevant quantum operations is investigated. It is shown that it is confined to an attractor space in which the resulting quantum Markov chain is diagonalizable. A construction procedure of a basis of this attractor space and its associated dual basis of 1-forms is presented. It is applicable whenever a strictly positive quantum state exists which is contracted or left invariant by the generating quantum operation. Moreover, algebraic relations between the attractor space and Kraus operators involved in the definition of a quantum Markov chain are derived. This construction is not only expected to offer significant computational advantages in cases in which the dimension of the Hilbert space is large and the dimension of the attractor space is small, but it also sheds new light onto the relation between the asymptotic dynamics of discrete quantum Markov chains and fixed points of their ge
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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