Quasifree stochastic cocycles and quantum random walks

TL;DR

This paper develops a theory of quasifree quantum stochastic calculus for infinite-dimensional noise, addressing uniqueness of covariance amplitudes and applying the results to identify quantum random walks driven by quasifree noises.

Contribution

It introduces a framework for quasifree stochastic calculus in infinite dimensions and links it to quantum random walks with quasifree noise limits.

Findings

Established uniqueness conditions for covariance amplitudes.

Connected quasifree cocycles to minimal stochastic dilations.

Identified classes of quantum random walks with quasifree noise limits.

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.