Quantum random walk revisited
Volume 73 / 2006
Banach Center Publications 73 (2006), 377-390
MSC: 81S25, 46N50, 60H10.
DOI: 10.4064/bc73-0-30
Abstract
In the framework of the symmetric Fock space over $L^2 ({\Bbb R}_{+}),$ the details of the approximation of the four fundamental quantum stochastic increments by the four appropriate spin-matrices are studied. Then this result is used to prove the strong convergence of a quantum random walk as a map from an initial algebra ${\cal A}$ into ${\cal A} \otimes {\cal B} \,(\hbox{Fock}\, (L^2 ({\Bbb R}_{+})))$ to a *-homomorphic quantum stochastic flow.
