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Coexistence does not imply Joint Measurability

David Reeb, Daniel Reitzner, Michael M. Wolf

J. Phys. A: Math. Theor. 46, 462002 , (2013)

DOI: doi:10.1088/1751-8113/46/46/462002 Pfeil
*arXiv.org*: arXiv:1307.6986 Pfeil

Abstract: The notion of coexistence of two observables was introduced by Ludwig in the context of analysing the possibility of measuring together observables, which are given in terms of positive operator-valued measures. It is known that joint measurability implies coexistence and that the converse holds at least in the case of two binary observables. This note clarifies whether or not this equivalence is also true for more than two outcomes. It isn't.