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

arXiv:1603.07740 · Physical Review A

Violation of Bell inequality based on S4 symmetry

Katarzyna Bolonek-Lasoń

Published Aug 9, 2016• 6 citations
arXivHTMLPDF

Abstract

In two recent papers [Phys. Rev. A 90, 062121 (2014) and Phys. Rev. A, 91, 052110 (2015)] an interesting method of analyzing the violation of Bell inequalities has been proposed which is based on the theory of finite group representations. Here we apply this method to more complicated examples of ${S}_{4}$ symmetry. We show how the Bell inequality can be related to the symmetries of regular tetrahedron. By choosing the orbits of three-dimensional representations of ${S}_{4}$ determined by the geometry of tetrahedron we find that the Bell inequality under consideration is violated in quantum theory. The corresponding nonlocal game is analyzed.

DOI
10.1103/physreva.94.022107

Related papers

Breaking of Bell inequality based on $S_4$ symmetry

Katarzyna Bolonek-Lasoń

In two recent papers (Phys. Rev. A90 (2014), 062121 and Phys. Rev. A91 (2015), 052110) an interesting method of analyzing the breaking of Bell inequalities has been proposed which is based on the theory of finite group representations. We apply here this method to more complicated example of $S_4$ symmetry. We show how the Bell inequality can be related to the symmetries of regular tetrahedron. By choosing the orbits of threedimensional representation of $S_4$ determined by the geometry of tetrahedron we find that the Bell inequality under consideration is broken in quantum theory. The corresponding nonlocal game is analyzed.

•Mar 24, 2016•1 citation

Violation of Bell inequalities from $$S_4$$ S 4 symmetry: the three orbits case

Katarzyna Bolonek-Lasoń, Ścibór Sobieski

The recently proposed (Güney and Hillery in Phys Rev A 90:062121, 2014; Phys Rev A 91:052110, 2015) group theoretical approach to the problem of violating the Bell inequalities is applied to $$S_4$$ group. The Bell inequalities based on the choice of three orbits in the representation space corresponding to standard representation of $$S_4$$ are derived and their violation is described. The corresponding nonlocal games are analyzed.

arXiv:1605.02322•Quantum Information Processing•Dec 27, 2016•5 citations

Bell Inequalities and Group Symmetry

Katarzyna Bolonek-Lasoń

Recently the method based on irreducible representations of finite groups has been proposed as a tool for investigating the more sophisticated versions of Bell inequalities (V. Ugǔr Gűney, M. Hillery, Phys. Rev. A90, 062121 ([2014]) and Phys. Rev. A91, 052110 ([2015])). In the present paper an example based on the symmetry group S 4 is considered. The Bell inequality violation due to the symmetry properties of regular tetrahedron is described. A nonlocal game based on the inequalities derived is described and it is shown that the violation of Bell inequality implies that the quantum strategies outperform their classical counterparts.

International Journal of Theoretical Physics•Mar 3, 2017•0 citations

Violation of Bell Inequalities for Multi-Parties

Yanmin Yang, Zhu‐Jun Zheng

In recent papers, the theory of representations of finite groups has been proposed to analyzing the violation of Bell inequalities. In this paper, we apply this method to more complicated cases. For two parties, Alice and Bob each make one of $d$ possible measurements, each measurement has $n$ outcomes, the Bell inequalities based on the choice of two orbits are derived. The classical bound is only dependent on the number of measurements, but the quantum bound is dependent both on $n$ and $d$. Even so, when $d$ is large enough, the quantum bound is only dependent on $d$. The subset of probabilities for four parties based on the choice of six orbits under group action is derived and its violation is described. Restricting the six orbits to three parties by forgetting the last party, and guaranteeing the classical bound invariant, the Bell inequality based on the choice of four orbits is derived. All the corresponding nonlocal games are analyzed.

•May 1, 2017•0 citations

Violation of Bell inequalities for multipartite systems

Yanmin Yang, Zhu‐Jun Zheng

In recent papers, the theory of representations of finite groups has been proposed to analyzing the violation of Bell inequalities. In this paper, we apply this method to more complicated cases. For two partite system, Alice and Bob each make one of $d$ possible measurements, each measurement has $n$ outcomes. The Bell inequalities based on the choice of two orbits are derived. The classical bound is only dependent on the number of measurements $d$, but the quantum bound is dependent both on $n$ and $d$. Even so, when $d$ is large enough, the quantum bound is only dependent on $d$. The subset of probabilities for four parties based on the choice of six orbits under group action is derived and its violation is described. Restricting the six orbits to three parties by forgetting the last party, and guaranteeing the classical bound invariant, the Bell inequality based on the choice of four orbits is derived. Moreover, all the corresponding nonlocal games are analyzed.

arXiv:1705.00513•May 1, 2017•0 citations

Bell inequalities for $S_4$ group: classical and quantum bounds for two orbits case

Katarzyna Bolonek-Lasoń, Piotr Kosiński

Within Guney-Hillery approach a number of examples of classical and quantum bounds on sum of probabilities resulting from two orbits of $S_4$ is considered. It is shown that the violation of Bell's inequalities is rather rare and gentle.

arXiv:1907.10437•Jul 24, 2019•0 citations
In two recent papers [Phys. Rev. A 90, 062121 (2014) and Phys. Rev. A, 91, 052110 (2015)] an interesting method of analyzing the violation of Bell inequalities has been proposed which is based on the theory of finite group representations. Here we apply this method to more complicated examples of S4{S}_{4}S4​ symmetry. We show how the Bell inequality can be related to the symmetries of regular tetrahedron. By choosing the orbits of three-dimensional representations of S4{S}_{4}S4​ determined by the geometry of tetrahedron we find that the Bell inequality under consideration is violated in quantum theory. The corresponding nonlocal game is analyzed.
Breaking of Bell inequality based on S4S_4S4​ symmetry
In two recent papers (Phys. Rev. A90 (2014), 062121 and Phys. Rev. A91 (2015), 052110) an interesting method of analyzing the breaking of Bell inequalities has been proposed which is based on the theory of finite group representations. We apply here this method to more complicated example of S4S_4S4​ symmetry. We show how the Bell inequality can be related to the symmetries of regular tetrahedron. By choosing the orbits of threedimensional representation of S4S_4S4​ determined by the geometry of tetrahedron we find that the Bell inequality under consideration is broken in quantum theory. The corresponding nonlocal game is analyzed.
Violation of Bell inequalities from S4S_4S4​ S 4 symmetry: the three orbits case
The recently proposed (Güney and Hillery in Phys Rev A 90:062121, 2014; Phys Rev A 91:052110, 2015) group theoretical approach to the problem of violating the Bell inequalities is applied to S4S_4S4​ group. The Bell inequalities based on the choice of three orbits in the representation space corresponding to standard representation of S4S_4S4​ are derived and their violation is described. The corresponding nonlocal games are analyzed.
Recently the method based on irreducible representations of finite groups has been proposed as a tool for investigating the more sophisticated versions of Bell inequalities (V. Ugǔr Gűney, M. Hillery, Phys. Rev. A90, 062121 ([2014]) and Phys. Rev. A91, 052110 ([2015])). In the present paper an example based on the symmetry group S 4 is considered. The Bell inequality violation due to the symmetry properties of regular tetrahedron is described. A nonlocal game based on the inequalities derived is described and it is shown that the violation of Bell inequality implies that the quantum strategies outperform their classical counterparts.
In recent papers, the theory of representations of finite groups has been proposed to analyzing the violation of Bell inequalities. In this paper, we apply this method to more complicated cases. For two parties, Alice and Bob each make one of ddd possible measurements, each measurement has nnn outcomes, the Bell inequalities based on the choice of two orbits are derived. The classical bound is only dependent on the number of measurements, but the quantum bound is dependent both on nnn and ddd. Even so, when ddd is large enough, the quantum bound is only dependent on ddd. The subset of probabilities for four parties based on the choice of six orbits under group action is derived and its violation is described. Restricting the six orbits to three parties by forgetting the last party, and guaranteeing the classical bound invariant, the Bell inequality based on the choice of four orbits is derived. All the corresponding nonlocal games are analyzed.
In recent papers, the theory of representations of finite groups has been proposed to analyzing the violation of Bell inequalities. In this paper, we apply this method to more complicated cases. For two partite system, Alice and Bob each make one of ddd possible measurements, each measurement has nnn outcomes. The Bell inequalities based on the choice of two orbits are derived. The classical bound is only dependent on the number of measurements ddd, but the quantum bound is dependent both on nnn and ddd. Even so, when ddd is large enough, the quantum bound is only dependent on ddd. The subset of probabilities for four parties based on the choice of six orbits under group action is derived and its violation is described. Restricting the six orbits to three parties by forgetting the last party, and guaranteeing the classical bound invariant, the Bell inequality based on the choice of four orbits is derived. Moreover, all the corresponding nonlocal games are analyzed.
Bell inequalities for S4S_4S4​ group: classical and quantum bounds for two orbits case
Within Guney-Hillery approach a number of examples of classical and quantum bounds on sum of probabilities resulting from two orbits of S4S_4S4​ is considered. It is shown that the violation of Bell's inequalities is rather rare and gentle.