Necessary Conditions for Extended Noncontextuality in General Sets of Random Variables
arXiv:1710.01318 · doi:10.1063/1.5024885
Abstract
We explore the graph approach to contextuality to restate the extended definition of noncontextuality as given by J. Kujala et. al. [Phys. Rev. Lett. 115, 150401 (2015)] using graph-theoretical terms. This extended definition avoids the assumption of the pre-sheaf or non-disturbance condition, which states that if two contexts overlap, then the marginal distribution obtained for the intersection must be the same, a restriction that will never be perfectly satisfied in real experiments. With this we are able to derive necessary conditions for extended noncontextuality for any set of random variables based on the geometrical aspects of the graph approach, which can be tested directly with experimental data in any contextuality experiment and which reduce to traditional necessary conditions for noncontextuality if the non-disturbance condition is satisfied.
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- Noncontextuality Inequalities from Antidistinguishability
- Graph Approach to Extended Contextuality
- From the problem of Future Contingents to Peres-Mermin square experiments: An introductory review to Contextuality
- Epistemic Odds of Contextuality in Cyclic Systems
- Contextuality and Informational Redundancy
- Contextuality with disturbance and without: Neither can violate substantive requirements the other satisfies
- Convexity of noncontextual wirings and how they order the set of correlations