Measurement incompatibility does not give rise to Bell violation in general

Erika Bene, Tamás Vértesi

Research output: Contribution to journalArticle

10 Citations (Scopus)


In the case of a pair of two-outcome measurements, incompatibility is equivalent to Bell nonlocality. Indeed, any pair of incompatible two-outcome measurements can violate the Clauser-Horne-Shimony-Holt Bell inequality, which has been proven by Wolf et al (2009 Phys. Rev. Lett. 103 230402). In the case of more than two measurements the equivalence between incompatibility and Bell nonlocality is still an open problem, though partial results have recently been obtained. Here we show that the equivalence breaks for a special choice of three measurements. In particular, we present a set of three incompatible two-outcome measurements, such that if Alice measures this set, independent of the set of measurements chosen by Bob and the state shared by them, the resulting statistics cannot violate any Bell inequality. On the other hand, complementing the above result, we exhibit a set of N measurements for any that is -wise compatible, nevertheless it gives rise to Bell violation.

Original languageEnglish
Article number013021
JournalNew Journal of Physics
Issue number1
Publication statusPublished - Jan 2018


  • Bell nonlocality
  • local hidden variable model
  • measurement incompatibility

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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