Some properties of partial fidelities

Basic properties of Uhlmann's partial fidelities are discussed. Statistical interpretation in terms of POVM measurements is established. Multiplicativity properties are considered. The relationship between partial fidelities and partitioned trace distances is derived. As it is shown, the partial fidelities cannot decrease under unistochastic quantum operations. Thus, the partial fidelities have good properties in the sense of their use as distinguishability measures.