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Entanglement and measurement in general probabilistic theories

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Quantum mechanics is a non-classical probability theory, but hardly the most general one imaginable: any compact convex set can serve as the state space for an abstract probabilistic model (classical models corresponding to simplices). From this altitude, one sees that many phenomena commonly regarded as ``characteristically quantum' are in fact generically ``non-classical'. In this talk, I'll show that almost any non-classical probabilistic theory shares with quantum mechanics a notion of entanglement and, with this, a version of the so-called measurement problem. I'll then discuss what's required for an abstract probabilistic theory to admit a somewhat simplified version of Everett's response to this problem -- an exercise that turns out to be instructive in several ways.