In the framework of the symmetric Fock space over L²(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 𝓐 into 𝓐 ⊗ ℬ (Fock(L²(ℝ₊))) to a *-homomorphic quantum stochastic flow.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-30,
author = {Kalyan B. Sinha},
title = {Quantum random walk revisited},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {377-390},
zbl = {1103.81030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-30}
}
Kalyan B. Sinha. Quantum random walk revisited. Banach Center Publications, Tome 72 (2006) pp. 377-390. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-30/