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Related papers: Contextuality with a Small Number of Observables

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We give some new explicit examples of putatively optimal projective spherical designs. i.e., ones for which there is numerical evidence that they are of minimal size. These form continuous families, and so have little apparent symmetry in…

Combinatorics · Mathematics 2025-03-20 Alex Elzenaar , Shayne Waldron

Quantum contextuality, as proved by Kochen and Specker, and also by Bell, should manifest itself in any state in any system with more than two distinguishable states and recently has been experimentally verified on various physical systems.…

Quantum Physics · Physics 2015-05-30 Sixia Yu , C. H. Oh

The Kochen-Specker theorem states that noncontextual hidden variable models are inconsistent with the quantum predictions for every yes-no question on a qutrit, corresponding to every projector in three dimensions. It has been suggested [D.…

Quantum Physics · Physics 2022-03-16 Adan Cabello , Jan-Åke Larsson

Kochen-Specker (KS) theorem denies the possibility for the noncontextual hidden variable theories to reproduce the predictions of quantum mechanics. A set of projection operators (projectors) and bases used to show the impossibility of…

Quantum Physics · Physics 2015-06-17 S. P. Toh

We study the geometry of the space of Mermin pentagrams, objects that are used to rule out the existence of noncontextual hidden variable theories as alternatives to quantum theory. It is shown that this space of 12096 possible pentagrams…

Quantum Physics · Physics 2017-01-27 Péter Lévay , Zsolt Szabó

We introduce an algebraic structure for studying state-independent contextuality arguments, a key form of quantum non-classicality exemplified by the well-known Peres-Mermin magic square, and used as a source of quantum advantage. We…

Quantum Physics · Physics 2026-03-16 Samson Abramsky , Serban-Ion Cercelescu , Carmen-Maria Constantin

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…

Quantum Physics · Physics 2012-08-15 Michel Planat

It has been recently shown that state-independent contextuality (SIC) is a fundamental resource linked with a type of nonlocality which cannot be improved by nonsignaling resources. Therefore, it is of fundamental importance to identify the…

Quantum Physics · Physics 2012-01-05 Adan Cabello

Quantum contextuality turns out to be a necessary resource for universal quantum computation and important in the field of quantum information processing. It is therefore of interest both for theoretical considerations and for experimental…

Quantum Physics · Physics 2017-09-19 Mladen Pavicic

Recent results show that Kochen-Specker (KS) sets of observables are fundamental to quantum information, computation, and foundations beyond previous expectations. Among KS sets, those that are unique up to unitary transformations (i.e.,…

Quantum Physics · Physics 2025-07-28 Stefan Trandafir , Adán Cabello

The Kochen-Specker theorem demonstrates that it is not possible to reproduce the predictions of quantum theory in terms of a hidden variable model where the hidden variables assign a value to every projector deterministically and…

Quantum Physics · Physics 2015-09-16 Ravi Kunjwal , Robert W. Spekkens

The claim of Meyer, Kent and Clifton (MKC) that finite precision measurement nullifies the Kochen-Specker theorem is criticised. It is argued that, although MKC have nullified the Kochen-Specker theorem strictly so-called, there are other,…

Quantum Physics · Physics 2007-05-23 D. M. Appleby

A "magic rectangle" of eleven observables of four qubits, employed by Harvey and Chryssanthacopoulos (2008) to prove the Bell-Kochen-Specker theorem in a 16-dimensional Hilbert space, is given a neat finite-geometrical reinterpretation in…

Quantum Physics · Physics 2012-07-31 Metod Saniga , Michel Planat

Quantum contextuality plays a significant role in supporting quantum computation and quantum information theory. The key tools for this are the Kochen--Specker and non-Kochen--Specker contextual sets. Traditionally, their representation has…

Quantum Physics · Physics 2025-01-17 Mladen Pavicic

In this paper from 2011 we approach some questions about quantum contextuality with tools from formal logic. In particular, we consider an experiment associated with the Peres-Mermin square. The language of all possible sequences of…

Logic in Computer Science · Computer Science 2020-04-23 Adán Cabello , Joost J. Joosten

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…

Quantum Physics · Physics 2023-12-05 Arthur C. R. Dutra , Roberto D. Baldijão , Marcelo Terra Cunha

The challenge of determining bounds for the minimal number of vectors in a three-dimensional Kochen-Specker (KS) set has captivated the quantum foundations community for decades. This paper establishes a weak lower bound of 10 vectors,…

Quantum Physics · Physics 2025-06-04 Tom Williams , Andrei Constantin

An essential ingredient in many examples of the conflict between quantum theory and noncontextual hidden variables (e.g., the proof of the Kochen-Specker theorem and Hardy's proof of Bell's theorem) is a set of atomic propositions about the…

Quantum Physics · Physics 2018-07-11 Adán Cabello , José R. Portillo , Alberto Solís , Karl Svozil

In 1960, the mathematician Ernst Specker described a simple example of nonclassical correlations which he dramatized using a parable about a seer who sets an impossible prediction task to his daughter's suitors. We revisit this example…

Quantum Physics · Physics 2018-05-16 Yeong-Cherng Liang , Robert W. Spekkens , Howard M. Wiseman

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…

Quantum Physics · Physics 2019-11-18 Mladen Pavicic