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It's easy enough to visualize and understand a pair of entangled particles, and how measuring the state of one instantly effects the state of the other. If the first is measured to be spin up for example, then the other will be spin down. But what if you have three entangled particles? How does measuring the first one effect the other two? Would measuring one collapse the superposition of all three? Or would the first one simply fall out of entanglement with the other two? Or is it as I suspect, that you can simply never have an odd number of entangled particles?

Every bit of logic and intuition that I have says that entanglement always results in an even number of particles. It has to. But logic and intuition can be wrong so I thought that I would ask someone who knows.

Can you ever have an odd number of entangled particles? If so, what happens when you measure one of an entangled triplet?

Thanks