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

Postselective quantum interference of distinguishable particles