Quantum Markov States and Quantum Hidden Markov States

In a previous paper (Funct. Anal. Appl., 3 (2015), 205–209), we defined quantum Markov states. Here we recall this definition and present a proof of the results from that paper (which are given there without proofs). We give a definition of a quantum hidden Markov state generated by a function of a...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 240; no. 5; pp. 507 - 514
Main Authors Bezhaeva, Z. I., Oseledets, V. I.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.08.2019
Springer
Springer Nature B.V
Subjects
Algebra
FUNCTIONS
GRAPH THEORY
Markov analysis
MARKOV PROCESS
Markov processes
MATHEMATICAL METHODS AND COMPUTING
Mathematics
Mathematics and Statistics
QUANTUM FIELD THEORY
QUANTUM STATES
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Summary:In a previous paper (Funct. Anal. Appl., 3 (2015), 205–209), we defined quantum Markov states. Here we recall this definition and present a proof of the results from that paper (which are given there without proofs). We give a definition of a quantum hidden Markov state generated by a function of a quantum Markov process and show how it is related to other definitions of such states. Our definitions work for quantum Markov fields on ℤ N and on graphs. We consider an example with the Cayley tree.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-019-04368-w