Cambalache 3,14 - La vidriera irrespetuosa

Adán Cabello, José R. Portillo, Alberto Solís, and Karl Svozil

Phys. Rev. A 98, 012106 – Published 5 July 2018

ABSTRACT An essential ingredient in many examples of the conflict between quantum theory and noncontextual hidden variables (e.g., the proof of the Kochen-Specker theorem and Hardy's proof of Bell's theorem) is a set of atomic propositions about the outcomes of ideal measurements such that, when outcome noncontextuality is assumed, if proposition A is true, then, due to exclusiveness and completeness, a nonexclusive proposition B (C) must be false (true). We call such a set a true-implies-false set (TIFS) [true-implies-true set (TITS)]. Here we identify all the minimal TIFSs and TITSs in every dimension d≥3 , i.e., the sets of each type having the smallest number of propositions. These sets are important because each of them leads to a proof of impossibility of noncontextual hidden variables and corresponds to a simple situation with quantum vs classical advantage. Moreover, the methods developed to identify them may be helpful to solve some open problems regarding minimal Kochen-Specker sets.