Simultaneous decomposition of two states

Simultaneous decompositions of a pair of states into pure ones are examined. There are privileged decompositions which are distinguished from all the other ones.Comment: 7 page

Fidelity preserving maps on density operators

We prove that any bijective fidelity preserving transformation on the set of all density operators on a Hilbert space is implemented by an either unitary or antiunitary operator on the underlying Hilbert space.Comment: This is corrected version of the paper math.OA/0108060. The paper has already appeared in ROMP (vol. 48 (2001), 299-303