Quantum random walks in one dimension
arXiv:quant-ph/0206053
Abstract
This letter treats the quantum random walk on the line determined by a 2 times 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 phi 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.
9 pages, journal reference added
References in corpus (2)
Cited by in corpus (23)
- Quantum Walks driven by many coins
- Quantum random walks with decoherent coins
- Quantum walks with an anisotropic coin I: spectral theory
- Quantum walks with an anisotropic coin II: scattering theory
- Localization for a one-dimensional split-step quantum walk with bound states robust against perturbations
- Convergence of continuous-time quantum walks on the line
- Quantum and random walks as universal generators of probability distributions
- Localization of the Grover walks on spidernets and free Meixner laws
- Path-integral solution of the one-dimensional Dirac quantum cellular automaton
- Maximal entanglement from quantum random walks
- The Witten Index for 1D Supersymmetric Quantum Walks with Anisotropic Coins
- A Constructive Approach to Topological Invariants for One-dimensional Strictly Local Operators
- Discrete time Dirac quantum walk in 3+1 dimensions
- Symmetry of distribution for the one-dimensional Hadamard walk
- Limit theorems and absorption problems for quantum random walks in one dimension
- Quantum Walks on the Line with Phase Parameters
- Localization of discrete-time quantum walks on a half line via the CGMV method
- A new type of quantum walks based on decomposing quantum states
- The time-averaged limit measure of the Wojcik model
- Invariance in Quantum Walks
- Fluctuations of Quantum Random Walks on Circles
- Limit theorems for the interference terms of discrete-time quantum walks on the line
- Crossover from Diffusive to Ballistic Transport in Periodic Quantum Maps