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Return Probability of the Open Quantum Random Walk with Time-Dependence

Clement Boateng Ampadu

We study the open quantum random walk (OQRW) with time-dependence on the one-dimensional lattice space and obtain the associated limit distribution. As an application we study the return probability of the OQRW. We also ask, "What is the average time for the return probability of the OQRW?"

Communications in Theoretical PhysicsMay 1, 20134 citations

Asymptotic Quantile Tukey-Lambda-Normality induced by the Hadamard Walk in the Central Limit Theorem of the Open Quantum Random Walk with Time Dependence

Clement Boateng Ampadu

Quantum Physics LettersApr 1, 20180 citations

Open quantum random walk in terms of quantum Bernoulli noise

Caishi Wang, Ce Wang, Suling Ren +1 more

Quantum Information ProcessingJan 23, 201812 citations

On the Structure of Quantum Markov Chains on Cayley Trees Associated with Open Quantum Random Walks

Abdessatar Souissi, Tarek Hamdi, Farrukh Maksutovich Mukhamedov +1 more

Quantum Markov chains (QMCs) and open quantum random walks (OQRWs) represent different quantum extensions of the classical Markov chain framework. QMCs stand as a more profound layer within the realm of Markovian dynamics. The exploration of both QMCs and OQRWs has been a predominant focus over the past decade. Recently, a significant connection between QMCs and OQRWs has been forged, yielding valuable applications. This bridge is particularly impactful when studying QMCs on tree structures, where it intersects with the realm of phase transitions in models naturally arising from quantum statistical mechanics. Furthermore, it aids in elucidating statistical properties, such as recurrence and clustering. The objective of this paper centers around delving into the intricate structure of QMCs on Cayley trees in relation to OQRWs. The foundational elements of this class of QMCs are built upon using classical probability measures that encompass the hierarchical nature of Cayley trees. This exploration unveils the pivotal role that the dynamics of OQRWs play in shaping the behavior of the Markov chains under consideration. Moreover, the analysis extends to their classical counterparts. The findings are further underscored by the examination of notable examples, contributing to a comprehensive understanding of the outcomes.Quantum Markov chains (QMCs) and open quantum random walks (OQRWs) represent different quantum extensions of the classical Markov chain framework. QMCs stand as a more profound layer within the realm of Markovian dynamics. The exploration of both QMCs and OQRWs has been a predominant focus over the past decade. Recently, a significant connection between QMCs and OQRWs has been forged, yielding valuable applications. This bridge is particularly impactful when studying QMCs on tree structures, where it intersects with the realm of phase transitions in models naturally arising from quantum statistical mechanics. Furthermore, it aids in elucidating statistical properties, such as recurrence and clustering. The objective of this paper centers around delving into the intricate structure of QMCs on Cayley trees in relation to OQRWs. The foundational elements of this class of QMCs are built upon using classical probability measures that encompass the hierarchical nature of Cayley trees. This exploration unveils the pivotal role that the dynamics of OQRWs play in shaping the behavior of the Markov chains under consideration. Moreover, the analysis extends to their classical counterparts. The findings are further underscored by the examination of notable examples, contributing to a comprehensive understanding of the outcomes.

AxiomsSep 7, 20234 citations

Limit Theorems for Open Quantum Random Walks

Norio Konno, Hyun Jae Yoo

arXiv:1209.1419Journal of Statistical PhysicsDec 13, 201251 citations

Hypergroup Structures of Open Quantum Random Walks on Distance Sets

Yusuke Sawada

Wildberger introduced the method of constructing a Hermitian discrete hypergroup from a random walk on a graph. In this study, we will apply his method to an open quantum random walk (OQRW) on a distance set and show that any discrete hypergroup that is not necessarily Hermitian can be realized using the OQRW on a distance set. We also investigate the distributions of OQRWs on distance sets in the view point of hypergroups.

arXiv:2009.09166Open Systems & Information DynamicsDec 1, 20231 citation

Return Probability of the Open Quantum Random Walk with Time-Dependence

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Return Probability of the Open Quantum Random Walk with Time-Dependence

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