A superposition principle for mixed states?

An approximate description of cyclic evolution of mixed states ρ (density matrices) is discussed in terms of vectors in R ⊗R (or Hilbert-Schmidt operators in R). It combines the decomposition ambiguity of ρ into pure states with the usual Berry phase for state vectors. The resulting non-Abelian quantum holonomy may be observable if the superposition principle is extended to R ⊗R © 1991 Società Italiana di Fisica.