Abstract
Using techniques from the study of quantum violations of Bell's inequalities, we give examples of three C *-algebras A, B, C, and states ω12 on A ⊗ B, and ω23 on B ⊗ C, which agree on B, but do not have a common extension to A ⊗ B ⊗ C. This situation cannot occur in classical probability, i.e. for commutative algebras.
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