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    Transition Probability (Fidelity) and Its Relatives.Armin Uhlmann - 2011 - Foundations of Physics 41 (3):288-298.
    Transition Probability (fidelity) for pairs of density operators can be defined as a “functor” in the hierarchy of “all” quantum systems and also within any quantum system. The Introduction of “amplitudes” for density operators allows for a more intuitive treatment of these quantities, also pointing to a natural parallel transport. The latter is governed by a remarkable gauge theory with strong relations to the Riemann-Bures metric.
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