  We have studied how the quality of transfer of a qubit state depends on
distinguishability of internal states of the particles carrying qubits. The
transfer is implemented without any direct interaction, just by a partial
exchange of photons, measurement on one of them, and conditional feed-forward
correction. It appears that the quality of the transfer is only influenced by
the level of distinguishability of the states of unaccessible internal degrees
of freedom not used for information encoding. We have found a directly
measurable parameter quantifying this level of distinguishability and proved it
usefulness experimentally.
