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Just a comment on:
“Similarly, that in a wavesplitter with a 50% wave in both arms there is no coincidence of particle detection.”
This statement is NOT general. If the electromagnetic field contains ONE photon, a 50% beam splitter could not show coincidences between two single photon detectors, but just a single detection in one of the detectors. If the field contains many photons, coincidences may be seen. If it contains just a few photons, rare coincidences can still be seen, due to the non-zero photon probability p(n).
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