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Quantum Information Processing

Mean hitting times of quantum Markov chains in terms of generalized inverses

  • 01-08-2019
Published in:
Author
Carlos F. Lardizabal
Published in
Quantum Information Processing | Issue 8/2019

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Abstract

We study quantum Markov chains on graphs, described by completely positive maps, following the model due to Gudder (J Math Phys 49:072105, 2008), which includes the dynamics given by open quantum random walks as defined by Attal et al. (J Stat Phys 147:832–852, 2012). After reviewing such structures, we examine a quantum notion of mean time of first visit to a chosen vertex. However, instead of making direct use of the definition as it is usually done, we focus on expressions for such quantity in terms of generalized inverses associated with the walk and most particularly the so-called fundamental matrix. Such objects are in close analogy with the theory of Markov chains, and the methods described here allow us to calculate examples that illustrate similarities and differences between the quantum and classical settings.

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next article Quantum data compression by principal component analysis
Title
Mean hitting times of quantum Markov chains in terms of generalized inverses
Author
Carlos F. Lardizabal
Publication date
01-08-2019
Publisher
Springer US
Published in
Quantum Information Processing / Issue 8/2019
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-019-2370-y
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This content is only visible if you are logged in and have the appropriate permissions.

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