Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Entropy

Engineering and Applying Quantum Contextuality

Mladen Pavičić

Published Apr 14, 2026• 0 citations
Publisher

Abstract

The endeavor to refute hidden variable theories underlying quantum theory has yielded the discipline of contextual sets. A plethora of various kinds of sets of arbitrary structure in any dimension have been developed, alongside extensive experimental validation. These advancements incited us to investigate to what extent we might move beyond hidden variables, engineer contextual sets, and find their applications within quantum theory itself, without any reference to hidden variable models. To this end, we consider possible applications of contextual sets in quantum computation, cryptography, pseudo-telepathy, and nonlocality, as well as generating them from error-correction protocols, complex Hadamard gates, and simple quantum gates. We found that the results in this field are still scarce, and we therefore investigated the directions in which future research might be carried out and the potential obstacles to realizing such undertakings in the past.

DOI
10.3390/e28040446

Related papers

Quantum Algorithms: A Survey of Applications and End-to-end Complexities

Alexander M. Dalzell, Sam McArdle, Mario Berta +10 more

The anticipated applications of quantum computers span across science and industry, ranging from quantum chemistry and many-body physics to optimization, finance, and machine learning. Proposed quantum solutions in these areas typically combine multiple quantum algorithmic primitives into an overall quantum algorithm, which must then incorporate the methods of quantum error correction and fault tolerance to be implemented correctly on quantum hardware. As such, it can be difficult to assess how much a particular application benefits from quantum computing, as the various approaches are often sensitive to intricate technical details about the underlying primitives and their complexities. Here we present a survey of several potential application areas of quantum algorithms and their underlying algorithmic primitives, carefully considering technical caveats and subtleties. We outline the challenges and opportunities in each area in an "end-to-end" fashion by clearly defining the problem being solved alongside the input-output model, instantiating all "oracles," and spelling out all hidden costs. We also compare quantum solutions against state-of-the-art classical methods and complexity-theoretic limitations to evaluate possible quantum speedups. The survey is written in a modular, wiki-like fashion to facilitate navigation of the content. Each primitive and application area is discussed in a standalone section, with its own bibliography of references and embedded hyperlinks that direct to other relevant sections. This structure mirrors that of complex quantum algorithms that involve several layers of abstraction, and it enables rapid evaluation of how end-to-end complexities are impacted when subroutines are altered.

arXiv:2310.03011•Oct 4, 2023•49 citations

Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions

Mladen Pavičić

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 been predominantly operator-based, mainly focusing on specific constructs in dimensions ranging from three to eight. However, nearly all of these constructs can be represented as low-dimensional hypergraphs. This study demonstrates how to generate contextual hypergraphs in any dimension using various methods, particularly those that do not scale in complexity with increasing dimensions. Furthermore, we introduce innovative examples of hypergraphs extending to dimension 32. Our methodology reveals the intricate structural properties of hypergraphs, enabling precise quantifications of contextuality. Additionally, we investigate several promising applications of hypergraphs in quantum communication and quantum computation, paving the way for future breakthroughs in the field.

arXiv:2501.09637•Entropy•Jan 9, 2025•1 citation

Contextualism and Nonlocality in the Algebra of EPR Observables

Federico Laudisa

The Bell 1964 theorem states that nonlocality is a necessary feature of hidden variable theories that reproduce the statistical predictions of quantum mechanics. In view of the no-go theorems for non-contextual hidden variable theories already existing up to 1964, and due to Gleason and Bell, one is forced to acknowledge the contextual character of the hidden variable theory which the Bell 1964 theorem refers to. Both the mathematical and the physical justifications of this contextualism are reconsidered. Consequently, the role of contextualism in recent no-hidden-variables proofs and the import of these proofs are investigated. With reference to the physical intuition underlying contextualism, the possibility is considered whether a context-dependence of individual measurement results is compatible with context-independence of the statistics of measurement results.

Philosophy of Science•Sep 1, 1997•13 citations

Epistemic Quantum Computational Structures in a Hilbert-space Environment

Enrico G. Beltrametti, María Luisa Dalla Chiara, Roberto Giuntini +2 more

Quantum computation and quantum computational logics are intrinsically connected with some puzzling epistemic problems. In the framework of a quantum computational approach to epistemic logic we investigate the following question: is it possible to i

Fundamenta Informaticae•Jan 1, 2012•20 citations

Quantum computation, discreteness, and contextuality

Robert Raussendorf

We establish a link between contextuality of quantum mechanics and quantum-mechanical computation. Specifically, we show that no deterministic measurement-based quantum compu-tation evaluating a non-linear function can be described by a non-contextual hidden-variable model. We give examples for such computations derived from quantum codes with suitable transversality properties, and from a counterexample to the LU-LC conjecture. 1

•Jul 31, 2009•2 citations

Two theorems of Jhon Bell and Communication Complexity

Guruprasad Kar

John Bell taught us that quantum mechanics can not be reproduced by non-contextual and local Hidden variable theory. The impossibility of replacing quantum mechanics by non-contextual Hidden Variable Theory can be turned to a impossible coloring pseudo-telepathy game to be played by two distant players. The game can not be won without communication in the classical world. But if the players share entangled state (quantum correlation) the game can be won deterministically using no communication. This again shows that though quantum correlation can not be used for communication, two parties can not simulate quantum correlation without classical communication. The motivation of the article is to present the earlier works on Hidden Variable Theory and recently developed pseudo-telepathy problem in a simpler way, which may be helpful for the beginners in this area.

arXiv:quant-ph/0504191•Apr 26, 2005•0 citations
The endeavor to refute hidden variable theories underlying quantum theory has yielded the discipline of contextual sets. A plethora of various kinds of sets of arbitrary structure in any dimension have been developed, alongside extensive experimental validation. These advancements incited us to investigate to what extent we might move beyond hidden variables, engineer contextual sets, and find their applications within quantum theory itself, without any reference to hidden variable models. To this end, we consider possible applications of contextual sets in quantum computation, cryptography, pseudo-telepathy, and nonlocality, as well as generating them from error-correction protocols, complex Hadamard gates, and simple quantum gates. We found that the results in this field are still scarce, and we therefore investigated the directions in which future research might be carried out and the potential obstacles to realizing such undertakings in the past.
The anticipated applications of quantum computers span across science and industry, ranging from quantum chemistry and many-body physics to optimization, finance, and machine learning. Proposed quantum solutions in these areas typically combine multiple quantum algorithmic primitives into an overall quantum algorithm, which must then incorporate the methods of quantum error correction and fault tolerance to be implemented correctly on quantum hardware. As such, it can be difficult to assess how much a particular application benefits from quantum computing, as the various approaches are often sensitive to intricate technical details about the underlying primitives and their complexities. Here we present a survey of several potential application areas of quantum algorithms and their underlying algorithmic primitives, carefully considering technical caveats and subtleties. We outline the challenges and opportunities in each area in an "end-to-end" fashion by clearly defining the problem being solved alongside the input-output model, instantiating all "oracles," and spelling out all hidden costs. We also compare quantum solutions against state-of-the-art classical methods and complexity-theoretic limitations to evaluate possible quantum speedups. The survey is written in a modular, wiki-like fashion to facilitate navigation of the content. Each primitive and application area is discussed in a standalone section, with its own bibliography of references and embedded hyperlinks that direct to other relevant sections. This structure mirrors that of complex quantum algorithms that involve several layers of abstraction, and it enables rapid evaluation of how end-to-end complexities are impacted when subroutines are altered.
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 been predominantly operator-based, mainly focusing on specific constructs in dimensions ranging from three to eight. However, nearly all of these constructs can be represented as low-dimensional hypergraphs. This study demonstrates how to generate contextual hypergraphs in any dimension using various methods, particularly those that do not scale in complexity with increasing dimensions. Furthermore, we introduce innovative examples of hypergraphs extending to dimension 32. Our methodology reveals the intricate structural properties of hypergraphs, enabling precise quantifications of contextuality. Additionally, we investigate several promising applications of hypergraphs in quantum communication and quantum computation, paving the way for future breakthroughs in the field.
The Bell 1964 theorem states that nonlocality is a necessary feature of hidden variable theories that reproduce the statistical predictions of quantum mechanics. In view of the no-go theorems for non-contextual hidden variable theories already existing up to 1964, and due to Gleason and Bell, one is forced to acknowledge the contextual character of the hidden variable theory which the Bell 1964 theorem refers to. Both the mathematical and the physical justifications of this contextualism are reconsidered. Consequently, the role of contextualism in recent no-hidden-variables proofs and the import of these proofs are investigated. With reference to the physical intuition underlying contextualism, the possibility is considered whether a context-dependence of individual measurement results is compatible with context-independence of the statistics of measurement results.
John Bell taught us that quantum mechanics can not be reproduced by non-contextual and local Hidden variable theory. The impossibility of replacing quantum mechanics by non-contextual Hidden Variable Theory can be turned to a impossible coloring pseudo-telepathy game to be played by two distant players. The game can not be won without communication in the classical world. But if the players share entangled state (quantum correlation) the game can be won deterministically using no communication. This again shows that though quantum correlation can not be used for communication, two parties can not simulate quantum correlation without classical communication. The motivation of the article is to present the earlier works on Hidden Variable Theory and recently developed pseudo-telepathy problem in a simpler way, which may be helpful for the beginners in this area.