Quasifree Stochastic Cocycles and Quantum Random Walks
Alexander C. R. Belton, Michał Gnacik, J. Martin Lindsay, Ping Zhong · Journal of Statistical Physics · 2019
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.