Related papers: The Limiting Distribution of Decoherent Quantum Ra…
In this paper we analyze the behavior of quantum random walks. In particular we present several new results for the absorption probabilities in systems with both one and two absorbing walls for the one-dimensional case. We compute these…
We consider discrete-time nearest-neighbor quantum walks on random environments in one dimension. Using the method based on a path counting, we present both quenched and annealed weak limit theorems for the quantum walk.
One-parameter family of discrete-time quantum-walk models on the square lattice, which includes the Grover-walk model as a special case, is analytically studied. Convergence in the long-time limit $t \to \infty$ of all joint moments of two…
We treat a quantum walk (QW) on the line whose quantum coin at each vertex tends to be the identity as the distance goes to infinity. We obtain a limit theorem that this QW exhibits localization with not an exponential but a "power-law"…
We study the entanglement dynamics of discrete time quantum walks acting on bounded finite sized graphs. We demonstrate that, depending on system parameters, the dynamics may be monotonic, oscillatory but highly regular, or quasi-periodic.…
It is well known that many real world networks have the power-law degree distribution (scale-free property). However there are no rigorous results for continuous-time quantum walks on such realistic graphs. In this paper, we analyze…
We study the decoherence effects originating from state flipping and depolarization for two-dimensional discrete-time quantum walks using four-state and two-state particles. By quantifying the quantum correlations between the particle and…
In this paper, we define a new type of decoherent quantum random walks with parameter $0\le p\le 1$, which becomes a unitary quantum random walk (UQRW) when $p=0$ and an open quantum random walk (OPRW) when $p=1$ respectively. We call this…
The mixing time of a discrete-time quantum walk on the hypercube is considered. The mean probability distribution of a Markov chain on a hypercube is known to mix to a uniform distribution in time O(n log n). We show that the mean…
Localization phenomena of quantum walks makes the propagation dynamics of a walker strikingly different from that corresponding to classical random walks. In this paper, we study the localization phenomena of four-state discrete-time…
We clarify that coined quantum walk is determined by only the choice of local quantum coins. To do so, we characterize coined quantum walks on graph by disjoint Euler circles with respect to symmetric arcs. In this paper, we introduce a new…
Quantum random walks, - coined, lattice ones, - exhibit ballistic behavior with fascinating asymptotic patterns of the amplitudes. We show that averaging over the coins (using the Haar measure), these patterns blend into a spline. Also, we…
Exploring the quantum walk as a tool of generating various probability distributions and quantum entanglements is a topic of current interest. In the present work, we use extensive numerical simulations to investigate the influence of…
The origin of the phenomenological deterministic laws that approximately govern the quasiclassical domain of familiar experience is considered in the context of the quantum mechanics of closed systems such as the universe as a whole. We…
The first general analytic solutions for the one-dimensional walk in position and momentum space are derived. These solutions reveal, among other things, new symmetry features of quantum walk probability densities and further insight into…
The discrete time quantum walk which is a quantum counterpart of random walk plays important roles in the theory of quantum information theory. In the present paper, we focus on discrete time quantum walks viewed as quantization of random…
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…
A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. Hitting times for discrete quantum walks on graphs give an average time before the walk…
We present a mathematical formalism for the description of unrestricted quantum walks with entangled coins and one walker. The numerical behaviour of such walks is examined when using a Bell state as the initial coin state, two different…
We study the behavior of a quantum gyroscope, that is, a quantum system which singles out a direction in space in order to measure certain properties of incoming particles such as the orientation of their spins. We show that repeated…