  There is a fundamental limit to what is knowable about atomic and molecular
scale systems. This fuzziness is not always due to the act of measurement.
Other contributing factors include system parameter uncertainty, functional
uncertainty that originates from input functions, and sensors noises to mention
a few. This indeterminism has led to major challenges in the development of
accurate control methods for atomic scale systems. To address the probabilistic
and uncertain nature of these systems, this work proposes a novel control
framework that considers the representation of the system quantum states and
the quantification of its physical properties following a probabilistic
approach. Our framework is fully probabilistic. It uses the Shannon relative
entropy from information theory to design optimal randomised controllers that
can achieve a desired outcome of an atomic scale system. Several experiments
are carried out to illustrate the applicability and effectiveness of the
proposed approach.
