Contextuality of General Probabilistic Theories

Generalized contextuality refers to our inability of explaining measurement statistics using a context-independent probabilistic and ontological model. On the other hand, can also be modeled framework general theories (GPTs). Here, starting from construction GPTs based on Gleason-type theorem, we fully characterize these structures with respect their permission rejection generalized (non)contextual models. It follows that in any GPT three insistence (i) no-restriction hypothesis, (ii) noncontextuality, (iii) multiple nonrefinable measurements for fixed number outcomes are incompatible. Hence, satisfying hypothesis is ontologically noncontextual if only it simplicial. We give detailed discussion which violated, show they always considered as subtheories (subGPTs) hypothesis. shown subGPTs simplicial same dimensionality. Finally, establish corollary necessary sufficient condition single resourceful or state promote an (i.e., classical) theory contextual nonclassical) one under hypothesis.Received 27 January 2020Revised 24 April 2020Accepted 11 2021DOI:https://doi.org/10.1103/PRXQuantum.2.010330Published by American Physical Society terms Creative Commons Attribution 4.0 International license. Further distribution this work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasQuantum formalismQuantum foundationsGeneral PhysicsQuantum Information