Broken Symmetries in the Entanglement of Formation
  We compare some recent computations of the entanglement of formation in quantum information theory and of the entropy of a subalgebra in quantum ergodic theory. Both notions require optimization over decompositions of quantum states. We show that both functionals are strongly related for some highly symmetric density matrices. We discuss the presence of broken symmetries in relation with the structure of the optimal decompositions. 
F. Benatti, H. Narnhofer, A. Uhlmann