Comparing the degrees of incompatibility inherent in probabilistic physical theories

Paul Busch, Teiko Heinosaari, Jussi Schultz, Neil Stevens

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We introduce a new way of quantifying the degrees of incompatibility of two observables in a probabilistic physical theory and, based in this, a global measure of the incompatibility of such theories. This open up an 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 incompatibility, for instance, by restricting the comparison to binary observables, it turns out that there are probabilistic theories that are more incompatible than quantum mechanics.
Original languageEnglish
Article number10002
Pages (from-to)1-17
JournalEurophysics Letters
Issue number1
Early online date18 Jul 2013
Publication statusPublished - Jul 2013


  • quant-ph

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