SpectraCat
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unusualname said:it's partially correct, but you can reduce background noise and use efficient entangled pair sources almost to make these effects negliglible.
The main reason for the coincidence counters is that only ~50% of a randomly polarised source of photons will pass through a polarizer (Malus' Law) and you can't know which will and which won't, so you must use coincidence counters. (similar probabilistic laws apply to wave plates and other apparatus)
People get confused because classically we couldn't measure individual photon detections.
That is not really correct. Coincidence counting is required because you have to correlate specific detection events at separate detectors with precise delay times in order to know with a high degree of certainty that two photons were generated as an entangled pair. Say for example you are sending one photon to Alice, who is 3 m away in the lab where the pair is generated, and the other photon to Bob, who is 150 m away in another building at the end of a fiber optic cable. So for a given entangled pair, the photons will arrive at the two detectors at different times ... you must have some way of knowing how to properly pair the separate detection events, and this is called coincidence counting.
The point about Malus' Law is something of a red herring, since most modern experiments with entanglement use polarizaing beam splitters (PBS's). A PBS sends photons with one polarization (say |H>) along one path to one detector, and those with the opposite polarization (say |V>) along a separate path to a separate detector. Both of those detectors are hooked to the coincidence counter, so both the |H> and |V> detection events can be captured in a single apparatus.
ow is the timing relevant for spatial coherence? Spatial coherence is mostly determined by the angular size of the source as "seen" by the detector.