We describe a two-photon quantum interference effect which differs from the Hong-Ou-Mandel effect in that the destructive quantum inference occurs on a component of the state where two photons are in a single output mode while maintaining the two-photon events in the alternative mode. This effect is manifestly nonclassical but requires more sophisticated technology to observe than the Hong-Ou-Mandel effect. The theory outlined in this paper can also be used to classify two-photon states into classes which are related by the ability to transform the states within the class by using only linear optical interactions. This theory shows that there is an infinite number of these classes of two photon states when there are two or more modes which can support the photons
