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JGWeissman comments on A note on the description complexity of physical theories - Less Wrong
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This "entanglement" is just Many Worlds applied to a subsystem rather than the whole universe. If you allow the entire universe to be involved in the entanglement, you are really talking about Many Worlds by another name. If you only allow subsystems to be entangled, you will make different predictions than Many Worlds.
The other name being "quantum mechanics." :D
Yes, if the typical interpretation of QM said anything about not allowing n-particle entangled states, it would be inconsistent with the math of quantum mechanics. But it doesn't, so it isn't. (Note that some people have made their own interpretations that violate this, e.g. consciousness causes collapse. They were wrong.)