Quantum walks have recently been introduced and investigated, with the hope that they may be useful in constructing new efficient quantum algorithms. For reviews of quantum walks, see Refs. [4, 16, 24]. There are two distinct types of the quantum walk: one is a discrete-time case [2, 5, 12, 14, 17, 18, 19, 22, 23], the other is a continuous-time case [1, 3, 7, 8, 10, 15, 20]. The quantum walk c...

Quantum Bernoulli random walks can be realized as random walks on the dual of SU(2). We use this realization in order to study a model of dynamic quantum Bernoulli random walk with time dependent transitions. For the corresponding dynamic random walk on the dual of SU(2), we prove several limit theorems (local limit theorem, central limit theorem, law of large numbers, large deviations principl...

Abstract Quantum random walks have been much studied recently, largely due to their highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum random walk on the line: the use of multiple quantum “coins” in order to diminish the effects of interference between paths. We find solutions to this system in terms of the single coin random ...

Recently, a formalism for discrete time open quantum walks was introduced [1]. The formalism suggested is similar to the formalism of quantum Markov chains and rests upon the implementation of appropriate completely positive maps. The formalism of the open quantum random walks (OQW) includes the classical random walk and through a physical realization procedure a connection to the unitary quant...

We introduce a multi-coin discrete quantum walk where the amplitude for a coin flip depends upon previous tosses. Although the corresponding classical random walk is unbiased, a bias can be introduced into the quantum walk by varying the history dependence. By mixing the biased walk with an unbiased one, the direction of the bias can be reversed leading to a new quantum version of Parrondo’s pa...

We consider a d-dimensional random quantum walk with site-dependent random coin operators. The corresponding transition coefficients are characterized by deterministic amplitudes times independent identically distributed site-dependent random phases. When the deterministic transition amplitudes are close enough to those of a quantum walk which forbids propagation, we prove that dynamical locali...

We consider a d-dimensional random quantum walk with site-dependent random coin operators. The corresponding transition coefficients are characterized by deterministic amplitudes times independent identically distributed site-dependent random phases. When the deterministic transition amplitudes are close enough to those of a quantum walk which forbids propagation, we prove that dynamical locali...