Quasifree stochastic cocycles and quantum random walks

Abstract

The theory of quasifree quantum stochastic calculus for infinite-dimensional noise is developed within the framework of Hudson-Parthasarathy quantum stochastic calculus. The question of uniqueness for the covariance amplitude with respect to which a given unitary quantum stochastic cocycle is quasifree is addressed, and related to the minimality of the corresponding stochastic dilation. The theory is applied to the identification of a wide class of quantum random walks whose limit processes are driven by quasifree noises.

Supported by the Leverhulme Trust Research Project Grant RPG-2014-196 Quantum Random Walks and Quasi-free Quantum Stochastic Calculus. 36 pages. Minor corrections have been made in version 2 which also contains references to several further articles. Further minor corrections, and bibliographical updates, made in version 3. To appear in the Journal of Statistical Physics