  We show that it is possible for completely distinguishable particles to
interfere postselectively without operating on, or indeed having any knowledge
of, the distinguishing degree of freedom. In particular, we find a family of
three-mode spatial interferometers that, upon inputting, say, a red photon in
port 1 and a green photon in port 2, produce a state such that when vacuum is
detected at one output, the two photons in the other two outputs will pass a
HOM test, despite their frequency degree of freedom remaining untouched. In
doing so we develop a general approach to distinguishability based on the
Schmidt decomposition between particles' "System" and "Label" degrees of
freedom, corresponding to what has been called unitary-unitary duality in
many-body physics. This also gives insight into the relationship between the
first and second quantized pictures, which is useful in bringing other quantum
information concepts across from the former to the latter.
