We extend the concept of distinguishability and likelihood introduced
by Englert in Phys. Rev. Lett. 77, 2154 (1996) to encompass quantum er
asure. We delineate the necessary and sufficient condition for obtaini
ng optimal values of distinguishability and erasure. Finally we apply
these measures on a gedanken welcher Weg experiment consisting of a co
upled atom-photon interferometer. [S1050-2947(98)08311-5].