相关论文: Asymptotic distributions of quantum walks on the l…

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…

This paper gives various asymptotic formulae for the transition probability associated with discrete time quantum walks on the real line. The formulae depend heavily on the `normalized' position of the walk. When the position is in the…

Discrete-time quantum walks are considered a counterpart of random walks and the study for them has been getting attention since around 2000. In this paper, we focus on a quantum walk which generates a probability distribution splitting to…

We offer theoretical explanations for some recent observations in numerical simulations of quantum random walks (QRW). Specifically, in the case of a QRW on the line with one particle (walker) and two entangled coins, we explain the…

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…

For a discrete two-state quantum walk (QW) on the half-line with a general condition at the boundary, we formulate and prove a weak limit theorem describing the terminal behavior of its transition probabilities. In this context,…

We analyze two families of three-state quantum walks which show the localization effect. We focus on the role of the initial coin state and its coherence in controlling the properties of the quantum walk. In particular, we show that the…

We study the asymptotic position distribution of general quantum walks on a lattice, including walks with a random coin, which is chosen from step to step by a general Markov chain. In the unitary (i.e., non-random) case, we allow any…

We perform the scattering analysis of the evolution operator of quantum walks with an anisotropic coin, and we prove a weak limit theorem for their asymptotic velocity. The quantum walks that we consider include one-defect models, two-phase…

In this article, we undertake a detailed study of the limiting behavior of a three-state discrete-time quantum walk on one dimensional lattice with generalized Grover coins. Two limit theorems are proved and consequently we show that the…

This paper continues the study of large time behavior of a nonlinear quantum walk begun in arXiv:1801.03214. In this paper, we provide a weak limit theorem for the distribution of the nonlinear quantum walk. The proof is based on the…

We present a comprehensive classification of one-dimensional coined quantum walks on the infinite line, focusing on the spatial probability distributions they induce. Building on prior results, we identify all initial coin states that lead…

We present numerical study of a model of quantum walk in periodic potential on the line. We take the simple view that different potentials affect differently the way the coin state of the walker is changed. For simplicity and definiteness,…

The quantum random walk has been much studied recently, largely due to its highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum walk on the line: the presence of decoherence…

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…

A unit evolution step of discrete-time quantum walks is determined by both a coin-flip operator and a position-shift operator. The behavior of quantum walkers after many steps delicately depends on the coin-flip operator and an initial…

The asymptotic behavior of the quantum walk on the line is investigated focusing on the probability distribution of chirality independently of position. The long-time limit of this distribution is shown to exist and to depend on the initial…

We investigate the ballistic spreading behavior of the one-dimensional discrete time quantum walks whose time evolution is driven by any balanced quantum coin. We obtain closed-form expressions for the long-time variance of position of…

We introduce the concept of a quantum walk with two particles and study it for the case of a discrete time walk on a line. A quantum walk with more than one particle may contain entanglement, thus offering a resource unavailable in the…

We focus on a 2-period time-dependent quantum walk on the half line in this paper. The quantum walker launches at the edge of the half line in a localized superposition state and its time evolution is carried out with two unitary operations…