I have read these questions and answers, and it made me curious
How does measurement affect multi-particle entangled particles?
How do particles become entangled?
None of these answered my question.
Question:
How can we (can we at all) create an entangled photon triplet?
In this case, any of the triplet's measuring would cause the collapse of the wavefunction for all other two particles?
Yes, 3 photon entangled states can be created. In fact 3 photon states can be "remotely prepared" using single photon measurement. See figure 1 for a description of this experiment. In this case the authors produce 4 entangled photons and send one to Alice and 3 to Bob. They show a beautiful example of the changes in Bob's state associated with Alice's single-photon measurement. A signal at Alice is able to infer entanglement of Bob's 3 photons. There are many related results, but hopefully this will give you a taste. Look up spontaneous parametric down-conversion if you want to understand the "magic" of nonlinear optics.
A nonlinear crystal such as BBO is used for parametric down-conversion. So a single, let's say, 1064 nm photon from a YAG laser produces 2 532 nm photons coming out of the BBO (or other nonlinear device). The two green photons are entangled. Here's a related SE question on how BBO creates entangled photons.
