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The "!" is the "partial measurement" operator. I am not expert in the field but as far as I understand the partial measurement is to collapse the superposition to one of the states relative to its amplitude (probability), while the post-selection operation is to choose the output state regardless its amplitude (probability). For example, measurement on a qubit in state 1/sqrt(2)(|0>+|1>) might give |0> or |1> with 50% chance, while to postselect |0> is to get |0> with 100% regardless its amplitude. Postselection gives you the power to choose the outcomes of certain measurements while normal measurement doesn't give you that power.


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