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Stephen comments on Which Basis Is More Fundamental? - Less Wrong
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Hal: "Somehow these kinds of correlations and influences happen while still not enabling FTL communication, but I don't know of anything in the formalism that clearly enforces this limitation."
The limitation of no FTL communication in quantum mechanics is called the no-signalling theorem. It is easy to prove using density matrices. I believe a good reference for this is the book by Nielsen & Chuang.