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Description

A significant part of quantum theory can be obtained by postulating a single conceptual innovation relative to classical theories, namely, that agents face a fundamental restriction on what they can know about the physical state of any system. This talk will consider a particular sort of statistical restriction wherein only classical variables with vanishing Poisson bracket can be known simultaneously. When this principle is applied to a classical statistical theory of three-level systems (trits), the resulting theory is found to be operationally equivalent to the stabilizer formalism for qutrits. Applied to a classical theory of harmonic oscillators, it yields quantum mechanics restricted to quadrature eigenstates and observables. Finally, applied to a classical statistical theory of bits, it yields a theory that is almost equivalent to (but interestingly different from) the stabilizer formalism for qubits. I will discuss the significance of these results for the project of deriving the formalism of quantum theory from physical principles.