Contextuality (or lack thereof) is a property of systems of random variables. Among the measures of the degree of contextuality, two have played important roles. One of them, Contextual Fraction ( $\text{CNTF}$ ) was proposed within the framework of the sheaf-theoretic approach to contextuality, and extended to arbitrary systems in the Contextuality-by-Default approach. The other, denoted $\text{CNT}_{2}$ , was proposed as one of the measures within the Contextuality-by-Default approach. In this note, I prove that $\text{CNTF}=2\text{CNT}_{2}$ within a class of systems, called cyclic, that have played a prominent role in contextuality research.Contextuality (or lack thereof) is a property of systems of random variables. Among the measures of the degree of contextuality, two have played important roles. One of them, Contextual Fraction ($\text{CNTF}$) was proposed within the framework of the sheaf-theoretic approach to contextuality, and extended to arbitrary systems in the Contextuality-by-Default approach. The other, denoted $\text{CNT}_{2}$, was proposed as one of the measures within the Contextuality-by-Default approach. In this note, I prove that $\text{CNTF}=2\text{CNT}_{2}$ within a class of systems, called cyclic, that have played a prominent role in contextuality research.

arXiv:2110.07113Oct 14, 20212 citations

Measures of contextuality in cyclic systems and the negative probabilities measure CNT3

Giulio Camillo, Victor Hernando Cervantes

Several principled measures of contextuality have been proposed for general systems of random variables (i.e. inconsistentlly connected systems). The first of such measures was based on quasi-couplings using negative probabilities (here denoted by CNT3, Dzhafarov & Kujala, 2016). Dzhafarov and Kujala (2019) introduced a measure of contextuality, CNT2, that naturally generalizes to a measure of non-contextuality. Dzhafarov and Kujala (2019) additionally conjectured that in the class of cyclic systems these two measures are proportional. Here we prove that that conjecture is correct. Recently, Cervantes (2023) showed the proportionality of CNT2 and the Contextual Fraction measure (CNTF) introduced by Abramsky, Barbosa, and Mansfeld (2017). The present proof completes the description of the interrelations of all contextuality measures as they pertain to cyclic systems.Several principled measures of contextuality have been proposed for general systems of random variables (i.e. inconsistentlly connected systems). The first of such measures was based on quasi-couplings using negative probabilities (here denoted by CNT3, Dzhafarov & Kujala, 2016). Dzhafarov and Kujala (2019) introduced a measure of contextuality, CNT2, that naturally generalizes to a measure of non-contextuality. Dzhafarov and Kujala (2019) additionally conjectured that in the class of cyclic systems these two measures are proportional. Here we prove that that conjecture is correct. Recently, Cervantes (2023) showed the proportionality of CNT2 and the Contextual Fraction measure (CNTF) introduced by Abramsky, Barbosa, and Mansfeld (2017). The present proof completes the description of the interrelations of all contextuality measures as they pertain to cyclic systems.

arXiv:2305.16574May 26, 20232 citations

Context-Dependence and Contextuality

Ehtibar N. Dzhafarov, Janne V. Kujala, Victor Hernando Cervantes

Cambridge University Press eBooksFeb 28, 20260 citations

A remark on the Kochen-Specker Theorem

Andrew Lenard

Springer eBooksJan 1, 19744 citations

The cohomological and the resource-theoretic perspective on quantum contextuality: common ground through the contextual fraction

Cihan Okay, Emily Tyhurst, Robert Raussendorf

We unify the resource-theoretic and the cohomological perspective on quantum contextuality. At the center of this unification stands the notion of the contextual fraction. For both symmetry and parity based contextuality proofs, we establish cohomological invariants which are witnesses of state-dependent contextuality. We provide two results invoking the contextual fraction, namely (i) refinements of logical contextuality inequalities, and (ii) upper bounds on the classical cost of Boolean function evaluation, given the contextual fraction of the corresponding measurement-based quantum computation.We unify the resource-theoretic and the cohomological perspective on quantum contextuality. At the center of this unification stands the notion of the contextual fraction. For both symmetry and parity based contextuality proofs, we establish cohomological invariants which are witnesses of state-dependent contextuality. We provide two results invoking the contextual fraction, namely (i) refinements of logical contextuality inequalities, and (ii) upper bounds on the classical cost of Boolean function evaluation, given the contextual fraction of the corresponding measurement-based quantum computation.

arXiv:1806.04657Quantum Information and ComputationDec 1, 201811 citations

Contextuality (or lack thereof) is a property of systems of random variables. Among the measures of the degree of contextuality, two have played important roles. One of them, Contextual Fraction (

\text{CNTF}

) was proposed within the framework of the sheaf-theoretic approach to contextuality, and extended to arbitrary systems in the Contextuality-by-Default approach. The other, denoted

\text{CNT}_{2}

, was proposed as one of the measures within the Contextuality-by-Default approach. In this note, I prove that

\text{CNTF}=2\text{CNT}_{2}

within a class of systems, called cyclic, that have played a prominent role in contextuality research.