  In this work, we show the ability to restore states of quantum systems from
evolution induced by quantum dynamical semigroups perturbed by covariant
measures. Our procedure describes reconstruction of quantum states transmitted
via quantum channels and as a particular example can be applied to
reconstruction of photonic states transmitted via optical fibers. For this, the
concept of perturbation by covariant operator-valued measure in a Banach space
is introduced and integral representation of the perturbed semigroup is
explicitly constructed. Various physically meaningful examples are provided. In
particular, a model of the perturbed dynamics in the symmetric (boson) Fock
space is developed as covariant measure for a semiflow of shifts and its
perturbation in the symmetric Fock space, and its properties are investigated.
Another example may correspond to the Koopman-von Neumann description of a
classical oscillator with bounded phase space.
