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Double-pair emission from type-II parametric down-conversion results in a highly entangled four-photon state. Due to interference, which is similar to bunching from thermal emission, this state is not simply a product of two pairs. The observation of this state can be achieved by splitting the two emission modes at beam splitters and subsequent detection of a photon in each output. Here we describe the features of this state and construct a Bell-type inequality, which gives a necessary and sufficient condition for a four-photon test of local realistic hidden variable theories.
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Weinfurter et al. (2001) studied this question.
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