Decoherence in quantum walks – a review
Mathematical Structures in Computer Science
Quantum Walks and Quantum Cellular Automata
ACRI '08 Proceedings of the 8th international conference on Cellular Automata for Reseach and Industry
One-dimensional discrete-time quantum walks on random environments
Quantum Information Processing
Quantum walks and elliptic integrals
Mathematical Structures in Computer Science
Localization of quantum walks on a deterministic recursive tree
Quantum Information & Computation
Localization of discrete-time quantum walks on a half line via the CGMV method
Quantum Information & Computation
Limit theorems for quantum walks with memory
Quantum Information & Computation
Limit theorems and absorption problems for quantum random walks in one dimension
Quantum Information & Computation
Maximal entanglement from quantum random walks
Quantum Information Processing
Crossovers induced by discrete-time quantum walks
Quantum Information & Computation
Return probability of one-dimensional discrete-time quantum walks with final-time dependence
Quantum Information & Computation
Entanglement for discrete-time quantum walks on the line
Quantum Information & Computation
Limit theorems for the discrete-time quantum walk on a graph with joined half lines
Quantum Information & Computation
Time averaged distribution of a discrete-time quantum walk on the path
Quantum Information Processing
Asymptotic distributions of quantum walks on the line with two entangled coins
Quantum Information Processing
Quantum walk on distinguishable non-interacting many-particles and indistinguishable two-particle
Quantum Information Processing
Quantum walks: a comprehensive review
Quantum Information Processing
Limit measures of inhomogeneous discrete-time quantum walks in one dimension
Quantum Information Processing
Limit theorems for the interference terms of discrete-time quantum walks on the line
Quantum Information & Computation
Hi-index | 0.00 |
This letter treats the quantum random walk on the line determined by a 2 × 2 unitary matrix U. A combinatorial expression for the mth moment of the quantum random walk is presented by using 4 matrices, P, Q, R and S given by U. The dependence of the mth moment on U and initial qubit state ϕ is clarified. A new type of limit theorems for the quantum walk is given. Furthermore necessary and sufficient conditions for symmetry of distribution for the quantum walk is presented. Our results show that the behavior of quantum random walk is striking different from that of the classical ramdom walk.PACS: 03.67.Lx; 05.40.Fb; 02.50.Cw