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The optical success probability of a fourfold GHZ source depends on the photon-number statistics of the assumed two-pair input. Let $q$ be the probability that arm $a$ contains one $H$ and one $V$, given two pairs. The beam splitter then puts one of the two $b$ photons into each output with probability $1/2$, and the final polarization-parity selection succeeds with probability $1/2$. With ideal photodetectors,For the normalized, fully overlapping two-pair component of polarization-entangled down-conversion used above, $q=1/3$, so the squared norm of the accepted component gives $P=1/12$. Treating the two emissions instead as independently labelled Bell pairs gives the commonly used bookkeeping estimate $q=1/2$ and $P=1/8$. This is a different pair-statistics approximation; it must not be obtained by dropping labels from an input state without renormalizing it. Genuine GHZ state coherence additionally requires erasing information about the pair of origin.

Let $P_2$ be the two-pair probability per pulse and $f$ the pulse repetition rate. The coincidence rate is $R=f{P}_{2}q/4$. With the usual order-of-magnitude estimate $P_2\simeq p^2$, the supplied $f=10^6{\mathrm{s}}^{-1}$ and $p=10^{-3}$ give $f{P}_2\simeq 1{\mathrm{s}}^{-1}$. The fully overlapping model gives $R\simeq 0.083{\mathrm{s}}^{-1}$, about one event per twelve seconds; independent-pair bookkeeping gives $R\simeq 0.125{\mathrm{s}}^{-1}$, about one per eight seconds. Thus the estimate is of order $10^{-1}{\mathrm{s}}^{-1}$ under these idealizations.

An exact prefactor cannot follow from the single-pair probability alone. For example, the pair-number statistics of polarization-entangled down-conversion in a single collected mode pair give $P_2\simeq 3p^2/4$ at weak gain, and hence $R\simeq f{p}^2/16=0.0625{\mathrm{s}}^{-1}$ with $q=1/3$. Multiple temporal or spectral modes change those statistics. Real collection losses and detector efficiencies further reduce the rate; they are excluded by the ideal calculation.