Open Quantum Random Walks

Dear colleagues,

Open Quantum Walks have been defined in the original article by Attal, Petruccione, Sabot and Sinayskiy in 2012. Since then Open Quantum Walks have known a very fast growing success. There have been many developments in the mathematical direction as well as towards physical applications.

These quantum walks are dissipative, as opposed to the usual Quantum Walks studied so far. The asymptotic behavior of Open Quantum Walks reflects this dissipative character, as has been shown in a Central Limit Theorem for Open Quantum Walks. Open Quantum Walks are the exact quantum extension of Markov chains; as such they allow to define extension of most of the Markov chain properties: recurrence, transience, exit time, potential theory, etc. Several extensions of the notion of Open Quantum Walks have also been successfully defined.

There have also been many developments and applications in Quantum Physics, with the Open Quantum Brownian motion, applications to continuous quantum measurement and to Open Quantum Systems more generally.

The aim of this special issue dedicated to Open Quantum Walks is to unit all the different authors interested in this fast growing subject, to make a state of the art of the recent developments. Original articles as well as small surveys of some specific aspect of Open Quantum Walks are accepted. 

Prof. Dr. Stephane Attal
Guest Editor

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