This paper relates cyclic cohomology, as obtained from traces with
domains on free product algebras, to the construction, by using the quantum
calculus of Hudson and Parthasarathy, of quantum (stochastic) flows. As
application of the methods of the present article, we show how the characters
finitely summable Fredholm modules, as constructed by Connes, can be recovered
from quantum flows in both the specialisation to the pure gauge and to
case. We also relate the regularized trace of Connes, used in the construction
these characters, to Lindblad generators.