  We trace back the phenomenon of "delayed-choice entanglement swapping" as it
was realized in a recent experiment to the commutativity of the projection
operators that are involved in the corresponding measurement process. We also
propose an experimental set-up which depends on the order of successive
measurements corresponding to noncommutative projection operators. In this case
entanglement swapping is used to teleport a quantum state from Alice to Bob,
where Bob has now the possibility to examine the noncommutativity within the
quantum history.
