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The 1999 experiment used an approximately $200\mathrm{fs}$, $394\mathrm{nm}$ pump pulse and a beta barium borate crystal. Two polarization-entangled photon pairs supplied four photons. A trigger and three other photodetectors selected a GHZ state through fourfold coincidence counting. Narrow interference filters lengthened the photon coherence time to approximately $500\mathrm{fs}$, exceeding the pump duration and suppressing timing information about which pair supplied which photon. The optical mode matching was essential to coherence, not merely to routing photons.^[ref]

The observed state was selected by all four detections, which also measured the photons. A trigger alone did not demonstrate a guaranteed surviving three-photon output. This distinction connects postselection to what an apparatus actually supplies, rather than identifying a fourfold coincidence with an unconditional source.^[ref]

The beta barium borate crystal supplies spontaneous parametric down-conversion: a weak ultraviolet pump can produce a pair of lower-frequency photons, with their frequencies and wavevectors selected by conservation of energy and phase matching. A suitably aligned and compensated source makes the two polarization alternatives coherent, giving the stated Bell state. The crystal alone does not guarantee that every collected pair has that state.

The two polarizing beam splitters route horizontal polarization and vertical polarization to different ports. Take $H$ from arm $a$ to the trigger $T$ and $V$ to arm $c$. The ordinary beam splitter in arm $b$ is a lossless, polarization-independent 50:50 splitter, with the unused input in the vacuum state. It splits probability amplitudes, rather than measuring which output a photon takes. The half-wave plate changes the relative phase of its principal polarizations by $\pi$; orient it so that a $V$ photon in $c$ becomes $(H+V)/\sqrt{2}$ in $c^{\prime }$, up to a common phase. Finally, photodetectors absorb arriving photons and supply electrical clicks. They need not resolve photon number for the ideal four-photon, fourfold-coincidence calculation: a click at every detector already requires one photon at each.

Choose the relative wave phases so that the final polarizing beam splitter sends $H_{c^{\prime }}$ to $H_2$, $V_{c^{\prime }}$ to $V_1$, $H_d$ to $H_1$ and $V_d$ to $V_2$. Such phase conventions must be used consistently: an uncompensated relative phase would give a phase-shifted GHZ state.