How (Maximally) Contextual is Quantum Mechanics?

Large violations in Kochen Specker contextuality and their applications

“…An open question has remained as to how contextual quantum mechanics is, when considering stateindependent non-contextuality inequalities, i.e., inequalities arising from KS proofs or from statistical stateindependent KS arguments. In [30], Simmons carried out mathematical investigations as to how (maximally) contextual is quantum mechanics, measuring this by the fraction of projectors in the KS proof that must have a valuation that depends on the context in which they are measured. An upper bound was derived on this quantity q(G) for arbitrary KS proofs in n-dimensional Hilbert space as [30]…”

“…In [30], Simmons carried out mathematical investigations as to how (maximally) contextual is quantum mechanics, measuring this by the fraction of projectors in the KS proof that must have a valuation that depends on the context in which they are measured. An upper bound was derived on this quantity q(G) for arbitrary KS proofs in n-dimensional Hilbert space as [30]…”

“…The authors made use of a graph-theoretic result by Feige [29] stating that for every > 0, an n-vertex graph G exists such that θ(G)/α(G) > n 1− to show that quantum theory allows for maximal contextuality in this case. In [30], Simmons studied how contextual quantum mechanics is when considering state-independent non-contextuality inequalities, as measured by the fraction of projectors in the KS proof that must have a valuation that depends on the context in which they are measured.…”

Roots and (re)sources of value (in)definiteness versus contextuality. A contribution to the Pitowsky Volume in memory of Itamar Pitowsky (1950--2010)

“…It is thereby granted that these considerations apply only to cases in which the assumptions of context independence are valid throughout the entire quantum cloud -that is, on for every observable in which contexts intertwine. If this were not the case -say, if only a single one observable occurring in intertwining contexts is allowed to be contextdependent [111,121] -the respective clouds taylored to prove Pitowsky's Logical Indeterminacy Principle and similar, as well as the Kochen-Specker theorems do not apply; and therefore the aforementioned consequences are invalid.…”