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The Hong-Ou-Mandel experiment is one of many examples where the amplitudes associated with two histories cancel out, leaving us with a reduced range of possible outcomes. Obviously, the total probability of those outcomes has to be unity.
My question relates to the fact that these processes are said to be unitary (i.e. conserve total probability). But when terms cancel as in HOM, we have to "manually" normalize the rest of the terms to get back to a total probability of 1. How then do we say that the transformation matrix itself is inherently unitary?
My question relates to the fact that these processes are said to be unitary (i.e. conserve total probability). But when terms cancel as in HOM, we have to "manually" normalize the rest of the terms to get back to a total probability of 1. How then do we say that the transformation matrix itself is inherently unitary?