Localization of M-Particle Quantum Walks

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 walkers at an initial location with high probability.Comment: To the authors knowledge, this paper appears to be the first to study the localization problem for a general M-Particle quantum walk. Will submit for publicatio

Sojourn Times for the One Dimensional Grover Walk

Using the technique of path counting we show non-existence of sojourn times in the Grover walk which is related to the Grover's algorithm in computer science.Comment: Conjectural Article. Contains an open problem, classifying all matrices up to general dimensionality with the property "non-existence of sojourn times implies localization

Brun-Type Formalism for Decoherence in Two Dimensional Quantum Walks

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 dimensional quantum walks, irrespective of the unitary transformation governing the walk. As an application we study decoherence in the presence of broken line noise in which the quantum walk is governed by the two-dimensional Hadamard operator.Comment: Presented as Poster Talk in "The International Meeting on Quantum Foundations and Quantum Information" at Seoul National Universit

Limit Theorems for the Disordered Quantum Walk

We study the disordered quantum walk in one dimension, and obtain the weak limit theorem.Comment: Contains an open proble

Spectral analysis of discrete-time quantum walks in the quarter plane

Using the Cantero-Grunbaum-Moral-Velazquez (CGMV) method, we obtain the spectral measure for the quantum walk.Comment: Contains an open problem showing the relationship between quantum walks in the quarter plane and quantum walks on homogeneous tree

Von Neumann Entanglement and Decoherence in Two Dimensional Quantum Walks

Using the concept of von Neumann entropy, we quantify the information content of the various components of the quantum walk system, including the mutual information between its subsystems (coin and position) and use it to give a precise formulation of the measure of entanglement between subsystems.Comment: It will be interesting to consider basic quantities of information theory to give a precise formulation of the measure of entanglement between subsytems (coin and position

On the Ambainis-Bach-Nayak-Vishwanath-Watrous Conjecture

We show the flaw in a theorem of Konno, Namiki, Soshi, and Sudbury in [3] and provide the necessary correction in the case of the Finite Hadamard walk and use it to show that a conjecture of Ambainis, Bach, Nayak, Vishwanath, and Watrous in [1] is false.Comment: 9 Pages, Accepted to appear in the Far East Journal of Applied Mathematic

Ito's formula for the discrete-time quantum walk in two dimensions

Following [Konno, arXiv:1112.4335], it is natural to ask: What is the Ito's formula for the discrete time quantum walk on a graph different than Z, the set of integers? In this paper we answer the question for the discrete time quantum walk on Z^2, the square lattice.Comment: Accepted for Publication in the Journal of Quantum Information Scienc

Limit Theorems For the Grover Walk Without Memory

We consider the Grover walk as a 4-state quantum walk without memory in one dimension. The walker in our 4-state quantum walk moves to the left or right. We compute the stationary distribution of the walk, in addition, we obtain the weak limit theoremComment: 15 pages, contains an extreme open proble

Limit Theorems for Quantum Walks on the Union of Planes

We extend the construction given by [Chisaki et.al, arXiv:1009.1306v1] from lines to planes, and obtain the associated limit theorems for quantum walks on such a graph.Comment: 22 page