Related papers: Gadget structures in proofs of the Kochen-Specker …
The Bell-Kochen-Specker theorem (BKS) theorem rules out realistic {\it non-contextual} theories by resorting to impossible assignments of rays among a selected set of maximal orthogonal bases. We investigate the geometrical structure of…
It is shown that, given a reasonable continuity assumption regarding possessed values, it is possible to construct a Kochen-Specker obstruction for any coordinate and its conjugate momentum, demonstrating that at most one of these two…
We performed an experimental test of the Kochen-Specker theorem based on an inequality derived from the Peres-Mermin proof, using spin-path (momentum) entanglement in a single neutron system. Following the strategy proposed by Cabello et…
This is a revision of my original posting, in which I raised objections to part of the Conway-Kochen argument. I now agree with them that their recent reply answers my original concerns. In the first part of these notes (identical to the…
The question of a hidden variable interpretation of quantum contextuality in the Mermin-Peres square is considered. The Kochen-Specker theorem implies that quantum mechanics may be interpreted as a contextual hidden variable theory. It is…
Commutativity gadgets provide a technique for lifting classical reductions between constraint satisfaction problems to quantum-sound reductions between the corresponding nonlocal games. We develop a general framework for commutativity…
Using a graph approach to quantum systems, we prove that descriptions of 3-dim Kochen-Specker (KS) setups as well as descriptions of 3-dim spin systems by means of Greechie lattices that we find in the literature are wrong. Correct lattices…
Quantum contextuality takes an important place amongst the concepts of quantum computing that bring an advantage over its classical counterpart. For a large class of contextuality proofs, aka. observable-based proofs of the Kochen-Specker…
Given a graph G, an incidence matrix N(G) is defined for the set of distinct isomorphism types of induced subgraphs of G. If Ulam's conjecture is true, then every graph invariant must be reconstructible from this matrix, even when the…
Using the spontaneous parametric down-conversion process in a type-I phase matching BBO crystal as single photon source, we perform an all-or-nothing-type Kochen-Specker experiment proposed by Simon \QTR{it}{et al}. [Phys. Rev. Lett.…
Quantum contextuality is a source of quantum computational power and a theoretical delimiter between classical and quantum structures. It has been substantiated by numerous experiments and prompted generation of state independent contextual…
In a previous paper, we have proposed assigning as the value of a physical quantity in quantum theory, a certain kind of set (a sieve) of quantities that are functions of the given quantity. The motivation was in part physical---such a…
Meyer recently queried whether non-contextual hidden variable models can, despite the Kochen-Specker theorem, simulate the predictions of quantum mechanics to within any fixed finite experimental precision. Clifton and Kent have presented…
Recently, Chattopadhyay et al. (\cite{chattopadhyay2017simulation}) proved that any gadget having so called \emph{hitting distributions} admits deterministic "query-to-communication" simulation theorem. They applied this result to Inner…
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…
Let $G\cong \mathbb Z/m_1\mathbb Z\times\ldots\times \mathbb Z/m_r\mathbb Z$ be a finite abelian group with $m_1\mid\ldots\mid m_r=\exp(G)$. The $n$-term subsums version of Kneser's Theorem, obtained either via the DeVos-Goddyn-Mohar…
The discovery of quantum key distribution by Bennett and Brassard (BB84) bases on the fundamental quantum feature: incompatibility of measurements of quantum non-commuting observables. In 1991 Ekert showed that cryptographic key can be…
We present a simple experimental scheme which can be used to demonstrate an all-or-nothing type contradiction between non-contextual hidden variables and quantum mechanics. The scheme, which is inspired by recent ideas by Cabello and…
k-graphs are higher-rank analogues of directed graphs which were first developed to provide combinatorial models for operator algebras of Cuntz-Krieger type. Here we develop a theory of the fundamental groupoid of a k-graph, and relate it…
We demonstrate that quantum instruments can provide a unified operational foundation for quantum theory. Since these instruments directly correspond to laboratory devices, this foundation provides an alternate, more experimentally grounded,…