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Consider the double-slit experiment except that the slits are imaginary. call the slits A and B.

you have a probability amplitude that a particles goes to the point x on the screen via A (an imaginary slit) and also an amplitude that it goes to the screen via B :

[tex] < xA | s > [/tex]

[tex] < xB | s > [/tex]

these two amplitudes are clearly the amplitudes for indistinguishable final states and therefore should interfere. but since the slits are imaginary, you could also write it as a single amplitude <x|s> and the probability is then just |<x|a>|^2.