CONVERGENCE OF COINED QUANTUM WALKS ON ℝd
Alex D. Gottlieb, Svante Janson, Petra F. Scudo · Infinite Dimensional Analysis Quantum Probability and Related Topics · 2005
Coined quantum walks may be interpreted as the motion in position space of a quantum particle with a spin degree of freedom; the dynamics are determined by iterating a unitary transformation which is the product of a spin transformation and a translation conditional on the spin state. Coined quantum walks on ℤd can be treated as special cases of coined quantum walks on ℝd. We study quantum walks on ℝd and prove that the sequence of rescaled probability distributions in position space associated to the unitary evolution of the particle converges to a limit distribution.