Summary
An approximate description of cyclic evolution of mixed states ρ (density matrices) is discussed in terms of vectors inR ⊗R (or Hilbert-Schmidt operators inR). 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 toR ⊗R
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We assume that no superselection rules are present.
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Dabrowski, L. A superposition principle for mixed states?. Nuov Cim B 106, 963–968 (1991). https://doi.org/10.1007/BF02728340
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DOI: https://doi.org/10.1007/BF02728340