How about this one... I have read of some attempts to create a 3 photon entangled state, but there is a lot of difficulty doing it. Could it be done by progressively splitting photons? 1. Generate a spin entangled photon pair from a standard parametric down conversion (PDC) setup. This "splits" one pump photon (say at 405 nanometers, a common source wavelength) in a H> & V> mixture passing through a pair of Type I (parallel output) BBO crystals aligned at 90 degrees to each other. The output photons are a pair of H>H> & V>V> at half the frequency (double the wavelength) of the pump photon, so they are now at 810 nm. 2. Take one of the photons (say the signal) in its superposition of H>H> & V>V>, and run it into another set of BBO crystals, tuned appropriately. 3. Would that create a new pair (at 1620 nm) in some mixed state like H>H>H> & V>V>V> ? With the original idler now in the same state? Admittedly, there would only be 3 output photons occasionally and therefore the source would seem pretty weak, maybe only 1 set out every 10 seconds. This is breaking my brain. Maybe you can't split such a photon yet again. Yet it seems like the only thing you need to create an entangled pair in the first place is an appropriate pump photon. If you did have 3 entangled photons, think of the Bell tests you could do on them! Might be pretty interesting. Vanesch, ZapperZ, someone...?