Unitary symmetries of open quantum systems trajectories

Abstract

We consider weak unitary symmetries of Markovian open quantum systems at the level of the joint dynamics of the system and its environment described by a continuous matrix product state, as well as for stochastic quantum trajectories of the system, obtained by conditioning on counting measurements of the environment. We derive necessary and sufficient conditions under which the dynamics of these different descriptions exhibit a weak symmetry, in turn characterising the resulting symmetries of their generators. In particular, this depends on whether the counting measurement satisfies the conditions we derive. In doing so we also consider the possible gauge transformations for generators of quantum trajectories, i.e. when two representations of the master operator produce equivalent trajectory ensembles.