Publications in Scientific Journals:
A. Cabello, R Portillo, A. Solis, K. Svozil:
"Minimal true-implies-false and true-implies-true sets of propositions in noncontextual hidden-variable theories";
Physical Review A,
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.
Minimale quantenmechanische Observablenmengen mit den wahr-impliziert-falsch, und wahr-impliziert-wahr Eigenschaften werden aufgezählt und diskutiert.
quantum logic, contextuality, quantum value indefiniteness
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
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Created from the Publication Database of the Vienna University of Technology.