scholarly journals From quantum graphs to quantum random walks

2006 ◽  
pp. 69-87 ◽  
Author(s):  
Gregor K. Tanner
Keyword(s):  
Random Walks ◽  
Quantum Graphs ◽  
Quantum Random Walks

scholarly journals One-dimensional quantum random walks with two entangled coins

2009 ◽  
Vol 79 (3) ◽  
Author(s):  
Chaobin Liu ◽  
Nelson Petulante
Keyword(s):  
Random Walks ◽  
Quantum Random Walks ◽  
One Dimensional

scholarly journals QUANTUM RANDOM WALKS AND TIME REVERSAL

1993 ◽  
Vol 08 (25) ◽  
pp. 4521-4545 ◽  
Author(s):  
S. MAJID
Keyword(s):  
Hopf Algebra ◽  
Random Walks ◽  
Hopf Algebras ◽  
Evolution Operator ◽  
Original System ◽  
Quantum Random Walks ◽  
Quantum Random Walk ◽  
Time Evolution Operator ◽  
Simple Physical Interpretation ◽  
Primitive Notion

Classical random walks and Markov processes are easily described by Hopf algebras. It is also known that groups and Hopf algebras (quantum groups) lead to classical and quantum diffusions. We study here the more primitive notion of a quantum random walk associated with a general Hopf algebra and show that it has a simple physical interpretation in quantum mechanics. This is by means of a representation theorem motivated from the theory of Kac algebras: If H is any Hopf algebra, it may be realized in Lin(H) in such a way that Δh=W(h⊗1)W−1 for an operator W. This W is interpreted as the time evolution operator for the system at time t coupled quantum-mechanically to the system at time t+δ. Finally, for every Hopf algebra there is a dual one, leading us to a duality operation for quantum random walks and quantum diffusions and a notion of the coentropy of an observable. The dual system has its time reversed with respect to the original system, leading us to a novel kind of CTP theorem.

Limit theorems and absorption problems for quantum radom walks in one dimension

2002 ◽  
Vol 2 (Special) ◽  
pp. 578-595
Author(s):  
N. Konno
Keyword(s):  
Random Walks ◽  
Limit Theorems ◽  
The Other ◽  
One Dimension ◽  
Unitary Matrices ◽  
Quantum Random Walks ◽  
One Dimensional ◽  
The Difference ◽  
The One

In this paper we consider limit theorems, symmetry of distribution, and absorption problems for two types of one-dimensional quantum random walks determined by $2 \times 2$ unitary matrices using our PQRS method. The one type was introduced by Gudder in 1988, and the other type was studied intensively by Ambainis et al. in 2001. The difference between both types of quantum random walks is also clarified.

scholarly journals Quantum Markov Chains Associated with Open Quantum Random Walks

2019 ◽  
Vol 176 (5) ◽  
pp. 1272-1295 ◽  
Author(s):  
Ameur Dhahri ◽  
Chul Ki Ko ◽  
Hyun Jae Yoo
Keyword(s):  
Markov Chains ◽  
Random Walks ◽  
Quantum Random Walks ◽  
Open Quantum ◽  
Open Quantum Random Walks ◽  
Quantum Markov Chains

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 Optical implementation of one-dimensional quantum random walks using orbital angular momentum of a single photon

2006 ◽  
Vol 8 (5) ◽  
pp. 81-81 ◽  
Author(s):  
Xubo Zou ◽  
Yuli Dong ◽  
Guangcan Guo
Keyword(s):  
Angular Momentum ◽  
Random Walks ◽  
Orbital Angular Momentum ◽  
Single Photon ◽  
Quantum Random Walks ◽  
One Dimensional

scholarly journals Quantum random walks on congested lattices and the effect of dephasing

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Keith R. Motes ◽  
Alexei Gilchrist ◽  
Peter P. Rohde
Keyword(s):  
Random Walks ◽  
Quantum Random Walks
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