1. Quantum Bochner theorems and incompatible observables
- Creator:
- Hudson, Robin L.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Bochner´s Theorem, multiplier-nonnegative- definiteness, Wigner quasidensities, and Pauli matrices
- Language:
- English
- Description:
- 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 explicitly in the spin case as the intersection of the Bloch sphere with a regular tetrahedron whose edges touch the sphere.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public