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Quantum States are Consistent Probability Distributions

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We describe a notion of state for a quantum system which is given in terms of a collection of empirically realizable probability distributions and is formally analogous to the familiar concept of state from classical statistical mechanics. We first demonstrate the mathematical equivalence of this new notion to the standard quantum notion of density matrix. We identify the simple logical consistency condition (a generalization of the familiar no-signalling condition) which a collection of distributions must obey in order to reconstruct the unique quantum state from which they arise. In this way, we achieve a formal expression of the common intuition of a quantum state as being classical distributions on compatible observables.