Remarks on joint distributions of observables
Kazimierz Urbanik (1987)
Colloquium Mathematicum
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Remarks on joint distributions of observables
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A quantum version of Bochner's theorem characterising Fourier transforms of probability measures on locally compact Abelian groups gives a characterisation of the Fourier transforms of Wigner quasi-joint distributions of position and momentum. An analogous quantum Bochner theorem characterises quasi-joint distributions of components of spin. In both cases quantum states in which a true distribution exists are characterised by the intersection of two convex sets. This may be described...