Related papers: Fine's theorem, noncontextuality, and correlations…
So far, most of the literature on (quantum) contextuality and the Kochen-Specker theorem seems either to concern particular examples of contextuality, or be considered as quantum logic. Here, we develop a general formalism for contextuality…
We show that under certain assumptions one can derive a variant of Specker's non-contextual inequality for a system of three indistinguishable bosonic particles. The inequality states that the sum of probabilities of three pairwise…
An operational definition of contextuality is introduced which generalizes the standard notion in three ways: (1) it applies to arbitrary operational theories rather than just quantum theory, (2) it applies to arbitrary experimental…
Contextuality is a key signature of quantum non-classicality, which has been shown to play a central role in enabling quantum advantage for a wide range of information-processing and computational tasks. We study the logic of contextuality…
Since the enlightening proofs of quantum contextuality first established by Kochen and Specker, and also by Bell, various simplified proofs have been constructed to exclude the non-contextual hidden variable theory of our nature at the…
In the paper it is shown that the Kochen-Specker theorem follows from Burnside's theorem on noncommutative algebras. Accordingly, contextuality (as an impossibility of assigning binary values to projection operators independently of their…
Bell non-locality and Kochen-Specker (KS) contextuality are logically independent concepts, fuel different protocols with quantum vs classical advantage, and have distinct classical simulation costs. A natural question is what are the…
For a hidden variable theory to be indistinguishable from quantum theory for finite precision measurements, it is enough that its predictions agree for some measurement within the range of precision. Meyer has recently pointed out that the…
KS-contextuality is a crucial feature of quantum theory. Previous research demonstrated the vanishing of $N$-cycle KS-contextuality in setups where multiple independent observers measure sequentially on the same system, which we call Public…
Contextuality is one way of capturing the non-classicality of quantum theory. The contextual nature of a theory is often witnessed via the violation of non-contextuality inequalities---certain linear inequalities involving probabilities of…
Nonlinear modifications of quantum theory are considered potential candidates for the theory of quantum gravity, with the intuitive argument that since Einstein field equations are nonlinear, quantum gravity should be nonlinear as well.…
The question of whether quantum phenomena can be explained by classical models with hidden variables is the subject of a long lasting debate. In 1964, Bell showed that certain types of classical models cannot explain the quantum mechanical…
Quantum processes cannot be reduced, in a nontrivial way, to classical processes without specifying the context in the description of a measurement procedure. This requirement is implied by the Kochen-Specker theorem in the…
Fine's theorem concerns the question of determining the conditions under which a certain set of probabilities for pairs of four bivalent quantities may be taken to be the marginals of an underlying probability distribution. The eight CHSH…
If the time evolution of a system can be understood classically, then there must exist an underlying probability distribution for the variables describing the system at all times. It is well known that for systems described by a single…
Quantum contextuality is one of the fundamental notions in quantum mechanics. Proofs of the Kochen-Specker theorem and noncontextuality inequalities are two means for revealing the contextuality phenomenon in quantum mechanics. It has been…
We provide the first systematic technique for deriving witnesses of contextuality in prepare-transform-measure scenarios. More specifically, we show how linear quantifier elimination can be used to compute a polytope of correlations…
Quantum theory has the intriguing feature that is inconsistent with noncontextual hidden variable models, for which the outcome of a measurement does not depend on which other compatible measurements are being performed concurrently. While…
In quantum theory, a measurement context is defined by an orthogonal basis in a Hilbert space, where each basis vector represents a specific measurement outcome. The precise quantitative relation between two different measurement contexts…
Quantum contextuality is the key concept which explains the fact that the result of a measurement is not independent of the context in which it is found. It is observed to be an intrinsic feature, i.e., neither entanglement nor spatial…