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We compare some recent computations of the entanglement of formation inquantum information theory and of the entropy of a subalgebra in quantumergodic theory. Both notions require optimization over decompositions ofquantum states. We show that both functionals are strongly related for somehighly symmetric density matrices. We discuss the presence of broken symmetriesin relation with the structure of the optimal decompositions.Comment: 21 pages, LateX, no figure

Broken symmetries in the entanglement of formation