Limit Theorems For Quantum Walks Associated with Hadamard Matrices
arXiv:1103.3899 · doi:10.1103/PhysRevA.84.012324
Abstract
We study a one-parameter family of discrete-time quantum walk models on the line and in the xy-plane associated with the Hadamard walk. Weak convergence in the long-time limit of all moments of the walker's pseudo-velocity on the line and in the xy-plane is proved. Symmetrization on the line and in the xy-plane is theoretically investigated, leading to the resolution of the Konno-Namiki-Soshi conjecture in the special case of symmetrization of the unbiased Hadamard walk on the line . A necessary condition for the existence of a phenomenon known as localization is given.
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- Limit Theorems for Quantum Walks on the Union of Planes