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 2 531 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.

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.