open quantum random walks
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2021 ◽  
pp. 2250001
Author(s):  
Ce Wang

Open quantum walks (OQWs) (also known as open quantum random walks) are quantum analogs of classical Markov chains in probability theory, and have potential application in quantum information and quantum computation. Quantum Bernoulli noises (QBNs) are annihilation and creation operators acting on Bernoulli functionals, and can be used as the environment of an open quantum system. In this paper, by using QBNs as the environment, we introduce an OQW on a general higher-dimensional integer lattice. We obtain a quantum channel representation of the walk, which shows that the walk is indeed an OQW. We prove that all the states of the walk are separable provided its initial state is separable. We also prove that, for some initial states, the walk has a limit probability distribution of higher-dimensional Gauss type. Finally, we show links between the walk and a unitary quantum walk recently introduced in terms of QBNs.





2019 ◽  
Vol 31 (07) ◽  
pp. 1950020 ◽  
Author(s):  
Ameur Dhahri ◽  
Farrukh Mukhamedov

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.



2019 ◽  
Vol 176 (5) ◽  
pp. 1272-1295 ◽  
Author(s):  
Ameur Dhahri ◽  
Chul Ki Ko ◽  
Hyun Jae Yoo


2019 ◽  
Vol 176 (3) ◽  
pp. 710-735
Author(s):  
Chul Ki Ko ◽  
Norio Konno ◽  
Etsuo Segawa ◽  
Hyun Jae Yoo








2015 ◽  
Vol 160 (5) ◽  
pp. 1125-1153 ◽  
Author(s):  
Raffaella Carbone ◽  
Yan Pautrat


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