English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study quantum Markov chains on graphs, described by completely positivemaps, following the model due to S. Gudder (J. Math. Phys. 49, 072105, 2008)and which includes the dynamics given by open quantum random walks as definedby S. Attal et al. (J. Stat. Phys. 147:832-852, 2012). After reviewing suchstructures we examine a quantum notion of mean time of first visit to a chosenvertex. However, instead of making direct use of the definition as it isusually done, we focus on expressions for such quantity in terms of generalizedinverses associated with the walk and most particularly the so-calledfundamental matrix. Such objects are in close analogy with the theory of Markovchains and the methods described here allow us to calculate examples thatillustrate similarities and differences between the quantum and classicalsettings.

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