GleasonType Derivations of the Quantum Probability Rule for Generalized Measurements
Abstract
We prove a Gleasontype theorem for the quantum probability rule using frame functions defined on positiveoperatorvalued measures (POVMs), as opposed to the restricted class of orthogonal projectionvalued measures used in the original theorem. The advantage of this method is that it works for twodimensional quantum systems (qubits) and even for vector spaces over rational fieldssettings where the standard theorem fails. Furthermore, unlike the method necessary for proving the original result, the present one is rather elementary. In the case of a qubit, we investigate similar results for frame functions defined upon various restricted classes of POVMs. For the socalled trine measurements, the standard quantum probability rule is again recovered.
 Publication:

Foundations of Physics
 Pub Date:
 February 2004
 DOI:
 10.1023/B:FOOP.0000019581.00318.a5
 arXiv:
 arXiv:quantph/0306179
 Bibcode:
 2004FoPh...34..193C
 Keywords:

 Quantum Physics
 EPrint:
 10 pages RevTeX, no figures