For a three-state quantum walk with a pairwise-coupling SU(3) coin (angles β, γ, with α fixed at π/4), spreading stays ballistic for all couplings while the speed and left-right asymmetry vary in structured ways across parameter space.
Limit theorems of a 3-state quantum walk and its application for discrete uniform measures
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abstract
We present two long-time limit theorems of a 3-state quantum walk on the line when the walker starts from the origin. One is a limit measure which is obtained from the probability distribution of the walk at a long-time limit, and the other is a convergence in distribution for the walker's position in a rescaled space by time. In addition, as an application of the walk, we obtain discrete uniform limit measures from the 3-state walk with a delocalized initial state.
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Controlled dynamics of a multi-component discrete-time quantum walker
For a three-state quantum walk with a pairwise-coupling SU(3) coin (angles β, γ, with α fixed at π/4), spreading stays ballistic for all couplings while the speed and left-right asymmetry vary in structured ways across parameter space.