  Stators, which may be intuitively defined as "half states, half operators"
are mathematical objects which act on two Hilbert spaces and utilize
entanglement to create remote operations and exchange information between two
physical systems. In particular, they allow to induce effective dynamics on one
physical system by acting on the other one, given they have properly been
connected with the right stator. In this work, the concept of stators is
generalized and formalized in a way that allows the utilization of stators for
some physical problems based on symmetry groups, and in particular digital
quantum simulation.
