Volume 103, Number 1, July 2013
|Number of page(s)||6|
|Published online||19 July 2013|
Comparing the degrees of incompatibility inherent in probabilistic physical theories
1 Department of Mathematics, University of York - York, YO10 5DD, UK, EU
2 Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku FI-20014 Turku, Finland, EU
3 Dipartimento di Matematica, Politecnico di Milano - Piazza Leonardo da Vinci 32, I-20133 Milano, Italy, EU
Received: 2 May 2013
Accepted: 19 June 2013
We introduce a new way of quantifying the degrees of incompatibility of two observables in a probabilistic physical theory and, based on this, a global measure of the degree of incompatibility inherent in such theories, across all observable pairs. This opens up a novel and flexible way of comparing probabilistic theories with respect to the nonclassical feature of incompatibility, raising many interesting questions, some of which will be answered here. We show that quantum theory contains observables that are as incompatible as any probabilistic physical theory can have if arbitrary pairs of observables are considered. If one adopts a more refined measure of the degree of incompatibility, for instance, by restricting the comparison to binary observables, it turns out that there are probabilistic theories whose inherent degrees of incompatibility are greater than that of quantum mechanics.
PACS: 03.65.Ta – Foundations of quantum mechanics; measurement theory
© EPLA, 2013
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