Luis Aina, Alfredo2023-06-202023-06-202004-11-291050-294710.1103/PhysRevA.70.052118https://hdl.handle.net/20.500.14352/51513©2004 The American Physical SocietyWe show the formal equivalence between the phase-space representations of transformations and quantum states. We study invariant quantum input-output transformations in phase space and in Hilbert space. We show that all invariant processes are linear transformations while the converse is not true. Some relevant examples of application of these ideas are examined.engjournal articlehttp://dx.doi.org/10.1103/PhysRevA.70.052118http://journals.aps.org/open access535Wigner distribution functionNoncommuting operatorsDensity-matrixQuasiprobability distributionsMacroscopic superpositionsProbability-distributionsState representationMechanicsDynamicsLightÓptica (Física)2209.19 Óptica Física