The way I understand it is when particles are entangled, when you measure one the entangled pair is instantly in a measured state. This question really goes to Copenhagen vs. MWI. If Eigenstates of the wave function are entangled, that seems to support MWI. If these Eigenstate are not entangled that could support Copenhagen. Here's a hypothetical. Say you have a wave function of the universe, if the Eigenstates are entangled then wouldn't each probable state exist? If Eigenstates are not entangled then you can have local universes with their own laws of physics made up of a combination of Eigenstates of the wave function of the universe and if these Eigenstates are not entangled, then every probable state wouldn't have to exist because on probable state is measured. Does this make any sense?