Related papers: Quantumness in decoherent quantum walk using measu…

We investigate the evolution of a discrete-time one-dimensional quantum walk driven by a position-dependent coin. The rotation angle which depends upon the position of a quantum particle parameterizes the coin operator. For different values…

We report on the possibility of controlling quantum random walks with a step-dependent coin. The coin is characterized by a (single) rotation angle. Considering different rotation angles, one can find diverse probability distributions for…

We quantitatively differentiate between the spreads of discrete-time quantum and classical random walks on a cyclic graph. Due to the closed nature of any cyclic graph, there is additional "collision"- like interference in the quantum…

The staggered quantum walk is a type of discrete-time quantum walk model without a coin which can be generated on a graph using particular partitions of the graph nodes. We design Hamiltonians for potential realization of the staggered…

We study a natural notion of decoherence on quantum random walks over the hypercube. We prove that in this model there is a decoherence threshold beneath which the essential properties of the hypercubic quantum walk, such as linear mixing…

We discuss the model of a one-dimensional, discrete-time walk on a line with spatial heterogeneity in the form of a variable set of ultrametric barriers. Inspired by the homogeneous quantum walk on a line, we develop a formalism by which…

We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which…

We study a 2-D disordered time-discrete quantum walk based on 1-D `generalized elephant quantum walk' where an entangling coin operator is assumed and which paves the way to a new set of properties. We show that considering a given disorder…

For a continuous-time quantum walk on a line the variance of the position observable grows quadratically in time, whereas, for its classical counterpart on the same graph, it exhibits a linear, diffusive, behaviour. A quantum walk, thus,…

We establish an operational connection between discrete rounds of generalized measurements and continuous-time decoherence, with an explicit correspondence between the number of measurement rounds and the evolution time. Operationally, we…

It is shown how to construct quantum random walks with particles in an arbitrary faithful normal state. A convergence theorem is obtained for such walks, which demonstrates a thermalisation effect: the limit cocycle obeys a quantum…

In quantum computation theory, quantum random walks have been utilized by many quantum search algorithms which provide improved performance over their classical counterparts. However, due to the importance of the quantum decoherence…

We present a discrete-time, one-dimensional quantum walk based on the entanglement between the momentum of ultracold rubidium atoms (the walk space) and two internal atomic states (the "coin" degree of freedom). Our scheme is highly…

We introduce a model for a two configurations system, and we study the transition from quantum to classical behaviour. We first consider the effect of the interaction with the environment as an external noise and we show that it produces…

We address the characterization of classical fractional random noise via quantum probes. In particular, we focus on estimation and discrimination problems involving the fractal dimension of the trajectories of a system subject to fractional…

Quantum walks behave differently from what we expect and their probability distributions have unique structures. They have localization, singularities, a gap, and so on. Those features have been discovered from the view point of mathematics…

Decoherence is the major stumbling block in the realization of a large-scale quantum computer. Ingenious methods have been devised to overcome decoherence, but their success has been proven only for over-simplified models of…

We use simple deterministic dynamical systems as coins in studying quantum walks. These dynamical systems can be chosen to display, in the classical limit, a range of behaviors from the integrable to chaotic, or deterministically random. As…

We study decoherence in the quantum walk on the xy-plane. We generalize the method of decoherent coin quantum walk, introduced by [T.A. Brun, et.al, Phys.Rev.A 67 (2003) 032304],which could be applicable to all sorts of decoherence in two…

In this paper, we study the discrete-time quantum random walks on a line subject to decoherence. The convergence of the rescaled position probability distribution $p(x,t)$ depends mainly on the spectrum of the superoperator…