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Main Author: Ishizaka, Satoshi
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2502.10746
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author Ishizaka, Satoshi
author_facet Ishizaka, Satoshi
contents It is difficult to establish an analytical criterion to identify the boundaries of quantum correlations, even for the simplest Bell scenario. Here, we briefly reviewed the plausible analytical criterion, and we found a way to confirm the extremal conditions from another direction. For that purpose, we analyzed the Navascués-Pironio-Ac\'ın (NPA) hierarchy to study the algebraic structure and found that the problem could not be simplified using $1\!+\!AB$ level. However, considering the plausible criterion, the $1\!+\!AB$ and second levels for correlations were equal, and the extremal condition in the simplest Bell scenario was replaced by that in the $1\!+\!AB$ level. Thus, the correctness of the plausible criterion was verified, and the results demonstrated that the plausible criterion held, thereby explaining its simplicity. It seemed plausible, but now it becomes more certain.
format Preprint
id arxiv_https___arxiv_org_abs_2502_10746
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle NPA Hierarchy and Extremal Criterion in the Simplest Bell Scenario
Ishizaka, Satoshi
Quantum Physics
It is difficult to establish an analytical criterion to identify the boundaries of quantum correlations, even for the simplest Bell scenario. Here, we briefly reviewed the plausible analytical criterion, and we found a way to confirm the extremal conditions from another direction. For that purpose, we analyzed the Navascués-Pironio-Ac\'ın (NPA) hierarchy to study the algebraic structure and found that the problem could not be simplified using $1\!+\!AB$ level. However, considering the plausible criterion, the $1\!+\!AB$ and second levels for correlations were equal, and the extremal condition in the simplest Bell scenario was replaced by that in the $1\!+\!AB$ level. Thus, the correctness of the plausible criterion was verified, and the results demonstrated that the plausible criterion held, thereby explaining its simplicity. It seemed plausible, but now it becomes more certain.
title NPA Hierarchy and Extremal Criterion in the Simplest Bell Scenario
topic Quantum Physics
url https://arxiv.org/abs/2502.10746