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Whilst reading this paper on a quantum processor that performs a type of matrix computation, I came across the concept of 'three-photon interference'. A quick Google search shows that this process is frequently referred to in quantum optical experiments but unfortunately, no wikipedia article exists for it, can anyone yield some insight on this?

My own guess is that it is exactly what it says: the interference pattern that results when 3 photons are combined. Why is this distinction so important?, why 3 photons and not 4, for example?

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I am not very familiar with the topic, but from searching reviewing some scientific publications, it just seems the interest come from being the simplest more-than-two photon interference. However it seems to be just one side of the full study of multiple photon interference (see book) – rmhleo Sep 14 '15 at 8:31

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