scholarly journals Open Quantum Random Walks: Ergodicity, Hitting Times, Gambler’s Ruin and Potential Theory

2016 ◽  
Vol 164 (5) ◽  
pp. 1122-1156 ◽  
Author(s):  
Carlos F. Lardizabal ◽  
Rafael R. Souza
Keyword(s):  
Random Walks ◽  
Potential Theory ◽  
Hitting Times ◽  
Quantum Random Walks ◽  
Open Quantum ◽  
Gambler’S Ruin ◽  
Open Quantum Random Walks

scholarly journals Open quantum random walks, quantum Markov chains and recurrence

2019 ◽  
Vol 31 (07) ◽  
pp. 1950020 ◽  
Author(s):  
Ameur Dhahri ◽  
Farrukh Mukhamedov
Keyword(s):  
Markov Chains ◽  
Random Walks ◽  
Markov Processes ◽  
Transition Operator ◽  
Quantum Random Walks ◽  
Open Quantum ◽  
Commutative Subalgebra ◽  
Open Quantum Random Walks ◽  
Quantum Markov Chains

In the present paper, we construct QMCs (Quantum Markov Chains) associated with Open Quantum Random Walks such that the transition operator of the chain is defined by OQRW and the restriction of QMC to the commutative subalgebra coincides with the distribution [Formula: see text] of OQRW. This sheds new light on some properties of the measure [Formula: see text]. As an example, we simply mention that the measure can be considered as a distribution of some functions of certain Markov processes. Furthermore, we study several properties of QMC and associated measures. A new notion of [Formula: see text]-recurrence of QMC is studied, and the relations between the concepts of recurrence introduced in this paper and the existing ones are established.

scholarly journals Open Quantum Random Walks

2012 ◽  
Vol 147 (4) ◽  
pp. 832-852 ◽  
Author(s):  
S. Attal ◽  
F. Petruccione ◽  
C. Sabot ◽  
I. Sinayskiy
Keyword(s):  
Random Walks ◽  
Quantum Random Walks ◽  
Open Quantum ◽  
Open Quantum Random Walks
Sign in / Sign up

Export Citation Format

Share Document