  On its own, the invariance by gauge transformations of Markovian master
equations has mostly played a mathematical or computational role in the
evaluation of quantum open system dynamics. So far, the fixation of a
particular gauge has only gained physical meaning when correlated with
additional information such as the results of measurements carried on over the
system or the environment in so-called quantum trajectories. Here, we show that
gauge transformations can be exploited, on their own, to optimize practical
physical tasks. To do so, first, we describe the inherent structure of the
underlying symmetries in quantum Markovian dynamics and present a general
formulation showing how they can be used to change the measurable values of
physical quantities. We then analyze examples of optimization in quantum
thermodynamics and, finally, we discuss the practical implementation of the
optimized protocols in terms of quantum trajectories.
