A semiclassically entangled puzzle
  For a maximally entangled eigenstate of a system of two non-interacting identical one dimensional harmonic oscilators, at the semiclassical level, it is not obviously true that a nonlinear interaction with one of the subsystems leaves the reduced semiclassical Wigner function of the other subsystem unaffected. Once stated, we advance some wild speculations regarding this seeming puzzle. 
Pedro de M. Rios