  I propose that non-Abelian topological order can emerge from the organization
of quantum particles into identical indistinguishable copies of the same
quantum many-body state. Quantum indistinguishability (symmetrization) of the
collectivities leads to topological degeneracy in the subspace of elementary
excitations, giving rise to non-Abelian braiding statistics. The non-Abelian
hidden order of a symmetrized structure is manifested in its entanglement
properties, and the corresponding non-Abelian fusion and braiding rules can be
derived by analyzing the set of symmetrized states on a surface with
non-trivial topology like a torus. To illustrate the emergence of non-Abelian
statistics from symmetrization, I consider the case of two identical copies of
the toric code model. The resulting model is shown to be non-Abelian,
exhibiting two types (charge and flux) of quasiparticles with non trivial
fusion channels. The symmetrization construction I present here constitutes a
framework for the generation of non-Abelian models from known Abelian ones.
