Related papers: Weak limits for quantum walks on the half-line
Recently Mc Gettrick [1] introduced and studied a discrete-time 2-state quantum walk (QW) with a memory in one dimension. He gave an expression for the amplitude of the QW by path counting method. Moreover he showed that the return…
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…
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 the motion of M particles performing a quantum walk on the line. Under various conditions on the initial coin states for quantum walkers controlled by the Hadamard operator, we give theoretical criterion to observe the quantum…
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.
An algebraic structure for one-dimensional quantum walks is introduced. This structure characterizes, in some sense, one-dimensional quantum walks. A natural computation using this algebraic structure leads us to obtain an effective formula…
Properties of the probability distribution generated by a discrete-time quantum walk, such as the number of peaks it contains, depend strongly on the choice of the initial condition. In the present paper we discuss from this point of view…
We investigate a generalized Hadamard walk in two dimensions with five inner states. The particle governed by a five-state quantum walk (5QW) moves, in superposition, either leftward, rightward, upward, or downward according to the inner…
We present two long-time limit theorems of a 3-state quantum walk on the line when the walker starts from the origin. One is a limit measure which is obtained from the probability distribution of the walk at a long-time limit, and the other…
In this article we continue the study of the quenched distributions of transient, one-dimensional random walks in a random environment. In a previous article we showed that while the quenched distributions of the hitting times do not…
Quantum walks are referred to as quantum analogs to random walks in mathematics. They have been studied as quantum algorithms in quantum information for quantum computers. There are two types of quantum walks. One is the discrete-time…
In this paper, the 2-state decomposed-type quantum walk (DQW) on a line is introduced as an extension of the 2-state quantum walk (QW). The time evolution of the DQW is defined with two different matrices, one is assigned to a real…
Since a limit distribution of a discrete-time quantum walk on the line was derived in 2002, a lot of limit theorems for quantum walks with a localized initial state have been reported. On the other hand, in quantum probability theory, there…
We study a generalized Hadamard walk in one dimension with three inner states. The particle governed by the three-state quantum walk moves, in superposition, both to the left and to the right according to the inner state. In addition to…
We observe that changing a phase at a single point in a discrete quantum walk results in a rather surprising localization effect. For certain values of this phase change the possibility of localization strongly depends on the internal…
This paper proves a weak limit theorem for a one-dimensional split-step quantum walk and investigates the limit density function. In the density function, the difference between two Konno's functions appears.
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…
The discrete-time quantum walk (QW) is determined by a unitary matrix whose component is complex number. Konno (2015) extended the QW to a walk whose component is quaternion.We call this model quaternionic quantum walk (QQW). The…
When confined to a topological environment consisting of a cycle coupled with a half-line, quantum walks exhibit long-term statistical tendencies which differ dramatically from the tendencies of classical random walks in the same…
We derive the weak limit theorem for a class of long range type quantum walks. To do it, we analyze spectral properties of a time evolution operator and prove that modified wave operators exist and are complete.