Onedimensional threestate quantum walk
Abstract
We study a generalized Hadamard walk in one dimension with three inner states. The particle governed by the threestate quantum walk moves, in superposition, both to the left and to the right according to the inner state. In addition to these two degrees of freedom, it is allowed to stay at the same position. We calculate rigorously the wave function of the particle starting from the origin for any initial qubit state and show the spatial distribution of probability of finding the particle. In contrast with the Hadamard walk with two inner states on a line, the probability of finding the particle at the origin does not converge to zero even after infinite time steps except special initial states. This implies that the particle is trapped near the origin after a long time with high probability.
 Publication:

Physical Review E
 Pub Date:
 November 2005
 DOI:
 10.1103/PhysRevE.72.056112
 arXiv:
 arXiv:quantph/0507207
 Bibcode:
 2005PhRvE..72e6112I
 Keywords:

 05.30.d;
 03.67.Lx;
 05.40.a;
 89.70.+c;
 Quantum statistical mechanics;
 Quantum computation;
 Fluctuation phenomena random processes noise and Brownian motion;
 Information theory and communication theory;
 Quantum Physics
 EPrint:
 16 pages, 3 figures