Limit Theorems For Quantum Walks Associated with Hadamard Matrices

Details Limit Theorems For Quantum Walks Associated with Hadamard Matrices Limit Theorems For Quantum Walks Associated with Hadamard Matrices

2011-03-20

arxiv.org/abs/1103.3899v4

Physical Review A, Volume 84, Number 1,012324 (2011)

Physics

Quantum Physics

Scientific paper

10.1103/PhysRevA.84.012324

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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