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Why can states and measurement outcomes be represented as vectors?

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arxiv quant-ph/0305117 v3 pith:FEZUSFDD submitted 2003-05-20 quant-ph

Why can states and measurement outcomes be represented as vectors?

classification quant-ph
keywords vectorsmeasurementoutcomessomestatesclassicalconnexionsdata
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It is shown how, given a "probability data table" for a quantum or classical system, the representation of states and measurement outcomes as vectors in a real vector space follows in a natural way. Some properties of the resulting sets of these vectors are discussed, as well as some connexions with the quantum-mechanical formalism.

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    The paper introduces the generalised probabilistic theories framework as a convex operational setting that represents states, transformations, and measurements and encompasses classical and quantum theories along with...