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Stators, which may be intuitively defined as "half states, half operators"are mathematical objects which act on two Hilbert spaces and utilizeentanglement to create remote operations and exchange information between twophysical systems. In particular, they allow to induce effective dynamics on onephysical system by acting on the other one, given they have properly beenconnected with the right stator. In this work, the concept of stators isgeneralized and formalized in a way that allows the utilization of stators forsome physical problems based on symmetry groups, and in particular digitalquantum simulation.

Half a state, half an operator: a general formulation of stators