Physical consequences of Lindbladian invariance transformations

On its own, the invariance properties of Markovian master equations have mostly played a mathematical or computational role in the evaluation of quantum open system dynamics. Because all forms of the equation lead to the same time evolution for the state of the system, the fixation of a particular form has only gained physical meaning when correlated with additional information such as in the evolution of quantum trajectories or the study of decoherence-free subspaces. Here, we show that these symmetry transformations can be exploited, on their own, to optimize practical physical tasks. In particular, we present a general formulation showing how they can be used to change the measurable values of physical quantities regarding the exchange of energy and/or information with the environment. We also analyze examples of optimization in quantum thermodynamics and, finally, discuss practical implementations in terms of quantum trajectories. Published by the American Physical Society 2024