On the existence of quantum representations for two dichotomic measurements
Abstract
Under which conditions do outcome probabilities of measurements possess a quantummechanical model? This kind of problem is solved here for the case of two dichotomic von Neumann measurements which can be applied repeatedly to a quantum system with trivial dynamics. The solution uses methods from the theory of operator algebras and the theory of moment problems. The ensuing conditions reveal surprisingly simple relations between certain quantummechanical probabilities. It also shown that generally, none of these relations holds in general probabilistic models. This result might facilitate further experimental discrimination between quantum mechanics and other general probabilistic theories.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 May 2010
 DOI:
 10.1063/1.3377969
 arXiv:
 arXiv:0908.2559
 Bibcode:
 2010JMP....51e2103F
 Keywords:

 03.65.Ta;
 03.65.Fd;
 02.50.Cw;
 02.10.v;
 Foundations of quantum mechanics;
 measurement theory;
 Algebraic methods;
 Probability theory;
 Logic set theory and algebra;
 Quantum Physics;
 Mathematical Physics
 EPrint:
 16+7 pages, presentation improved and minor errors corrected