Exploring Quantum contextuality with the quantum Möbius-Escher-Penrose hypergraph

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F25%3A00383377" target="_blank" >RIV/68407700:21230/25:00383377 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1103/PhysRevA.111.042209" target="_blank" >https://doi.org/10.1103/PhysRevA.111.042209</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1103/PhysRevA.111.042209" target="_blank" >10.1103/PhysRevA.111.042209</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Exploring Quantum contextuality with the quantum Möbius-Escher-Penrose hypergraph

Popis výsledku v původním jazyce

This paper presents the quantum Möbius-Escher-Penrose hypergraph, drawing inspiration from paradoxical constructs such as the Möbius strip and Penrose’s “impossible objects.” The hypergraph is constructed using faithful orthogonal representations in Hilbert space, thereby embedding the graph within a quantum framework. Additionally, a quasiclassical realization is achieved through two-valued states and partition logic, leading to an embedding within a Boolean algebra. This dual representation delineates the distinctions between classical and quantum embeddings, with a particular focus on contextuality, highlighted by violations of exclusivity and completeness, quantified through classical and quantum probabilities. The paper also examines violations of Boole’s conditions of possible experience using correlation polytopes, underscoring the inherent contextuality of the hypergraph. These results offer deeper insights into quantum contextuality and its intricate relationship with classical logic structures.

Název v anglickém jazyce

Exploring Quantum contextuality with the quantum Möbius-Escher-Penrose hypergraph

Popis výsledku anglicky

This paper presents the quantum Möbius-Escher-Penrose hypergraph, drawing inspiration from paradoxical constructs such as the Möbius strip and Penrose’s “impossible objects.” The hypergraph is constructed using faithful orthogonal representations in Hilbert space, thereby embedding the graph within a quantum framework. Additionally, a quasiclassical realization is achieved through two-valued states and partition logic, leading to an embedding within a Boolean algebra. This dual representation delineates the distinctions between classical and quantum embeddings, with a particular focus on contextuality, highlighted by violations of exclusivity and completeness, quantified through classical and quantum probabilities. The paper also examines violations of Boole’s conditions of possible experience using correlation polytopes, underscoring the inherent contextuality of the hypergraph. These results offer deeper insights into quantum contextuality and its intricate relationship with classical logic structures.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

PHYSICAL REVIEW A

ISSN

2469-9926

e-ISSN

2469-9934

Svazek periodika

111

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

8

Strana od-do

—

Kód UT WoS článku

001491903800006

EID výsledku v databázi Scopus

2-s2.0-105003026900