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Transition Probability (Fidelity) and Its Relatives

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Abstract

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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  1. Institute for Theoretical Physics, University of Leipzig, PB 100920, 04009, Leipzig, Germany

    Armin Uhlmann

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  1. Armin Uhlmann
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Uhlmann, A. Transition Probability (Fidelity) and Its Relatives. Found Phys 41, 288–298 (2011). https://doi.org/10.1007/s10701-009-9381-y

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