Related papers: Contextuality with a Small Number of Observables
This paper is the first of several parts introducing a new powerful algebra: the algebra of the pseudo-observables. This is a C*-algebra whose set is formed by formal expressions involving observables. The algebra is constructed by applying…
Recently, quantum contextuality has been proved to be the source of quantum computation's power. That, together with multiple recent contextual experiments, prompts improving the methods of generation of contextual sets and finding their…
The Kochen-Specker theorem rules out models of quantum theory wherein projective measurements are assigned outcomes deterministically and independently of context. This notion of noncontextuality is not applicable to experimental…
We classify the sets of natural numbers $n$ for which certain dynamical systems $(X,f)$ on a compact metric space $X$ have a periodic point of (least) period $n$. Interest in this question dates back to Sharkovskii's theorem for continuous…
Composing two representations of the general linear groups gives rise to Littlewood's (outer) plethysm. On the level of characters, this poses the question of finding the Schur expansion of the plethysm of two Schur functions. A…
Combining the tools of geometric analysis with properties of Jordan angles and angle space distributions, we derive a spherical and a Euclidean Bernstein theorem for minimal submanifolds of arbitrary dimension and codimension, under the…
The Kochen-Specker theorem is a fundamental result in quantum foundations that has spawned massive interest since its inception. We show that within every Kochen-Specker graph, there exist interesting subgraphs which we term $01$-gadgets,…
A physical applicability of normed split-algebras, such as hyperbolic numbers, split-quaternions and split-octonions is considered. We argue that the observable geometry can be described by the algebra of split-octonions. In such a picture…
We find many tight codes in compact spaces, i.e., optimal codes whose optimality follows from linear programming bounds. In particular, we show the existence (and abundance) of several hitherto unknown families of simplices in quaternionic…
We present a new and feasible test proving quantum contextuality in four-dimensional Hiltbert space. In our scheme, a contradiction between quantum mechanics and noncontextual hidden variables is revealed through the measurement statistics…
The non-classicality of single quantum systems can be formalised using the notion of contextuality. But can contextuality be convincingly demonstrated in an experiment, without reference to the quantum formalism? The operational approach to…
Theorems crucial in elementary real function theory have proofs in which compactness arguments are used. Despite the introduction in relatively recent literature of each new highly elegant compactness argument, or of an equivalent, this…
Compatibility between the realist tenants of value-definiteness and causality is called into question by several realism impossibility proofs in which their formal elements are shown to conflict. We review how this comes about in the…
Minimal surfaces and domain walls play important roles in various contexts of spacetime physics as well as material science. In this paper, we first review the Bernstein conjecture, which asserts that a plane is the only globally well…
Contextuality is regarded as a non-classical feature, challenging our everyday intuition; quantum contextuality is currently seen as a resource for many applications in quantum computation, being responsible for quantum advantage over…
We combine several mini miracles to achieve an elementary understanding of infinite loop spaces and very effective spectra in the algebro-geometric setting of motivic homotopy theory. Our approach combines $\Gamma$-spaces and framed…
Quantum mechanics implies that not all physical properties can be simultaneously well defined, such as the momentum and position due to Heisenberg uncertainty principle. Some alternative theories have been explored, notably the…
We show that a reduced form of the structural requirements for deterministic hidden variables used in Bell-Kochen-Specker theorems is already sufficient for the no-go results. Those requirements are captured by the following principle: an…
Contextuality is a fundamental marker of quantum non-classicality, which has emerged as a key resource for quantum computational advantage in multiple settings. Many such results hinge specifically on contextuality witnessed through Pauli…
Kent [quant-ph/9906006] has constructed a hidden variable theory by taking the finite precision of physical measurements into account. But its claim to noncontextuality has been queried, and it shown here that there is a particularly simple…