On the existence of quantum representations for two dichotomic measurements

Details On the existence of quantum representations for two dichotomic measurements On the existence of quantum representations for two dichotomic measurements

2009-08-18

arxiv.org/abs/0908.2559v2

J. Math. Phys. 51, 052103 (2010)

Physics

Quantum Physics

16+7 pages, presentation improved and minor errors corrected

Scientific paper

10.1063/1.3377969

Under which conditions do outcome probabilities of measurements possess a quantum-mechanical 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 quantum-mechanical 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.

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