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Yes, you are on the right track. Locally, there is only local density matrix. It captures all information about what is there. And it cannot be changed by action at a distance.
But, all local density matrices do not exhaust all the ontology. Wave function is more than this. And in some sense it is non-local (entanglement etc.). However, local density matrix is certainly real as it ALL what is in a particular location. If something in this location entangled with something in other location, local interaction might lead to entanglement to more systems, but no change happens nonlocally: no action at a distance!
I am preparing a talk “Ontology of the wave function”, Saig, July 22. If it will be recorded in some way I’ll send you a link.
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