= Optical success probability of a fourfold GHZ source
{title2=$P_{\mathrm{fourfold}\mid2\,\mathrm{pairs}}=q/4$}
For a source with exactly two photons in each input arm, let $q$ be the probability of one horizontal and one vertical photon in the trigger arm. This sector alone supplies exactly one trigger photon. Splitting the other arm across its two output ports has probability $1/2$; the final <polarizing beam splitter> selects equal polarizations with probability $1/2$. The fourfold success probability is therefore $q/4$. The <two-pair component of polarization-entangled down-conversion> has $q=1/3$, giving $1/12$; independent pair bookkeeping has $q=1/2$, giving $1/8$. Pair-label distinguishability can also destroy the conditional <GHZ state> coherence and must be checked separately.
Back to article page
