1. Quantum Markov States and Quantum Hidden Markov States
- Author
-
Z. I. Bezhaeva and V. I. Oseledets
- Subjects
Statistics and Probability ,Discrete mathematics ,Markov chain ,Applied Mathematics ,General Mathematics ,Markov process ,Function (mathematics) ,State (functional analysis) ,Mathematical proof ,Tree (graph theory) ,symbols.namesake ,symbols ,Hidden Markov model ,Quantum ,Mathematics - Abstract
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 ℤN and on graphs. We consider an example with the Cayley tree.
- Published
- 2019