NPA Hierarchy and Extremal Criterion in the Simplest Bell Scenario
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,...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-02-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/27/2/182 |
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| Summary: | 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-Acín (NPA) hierarchy to study the algebraic structure and found that the problem could not be simplified using the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>+</mo><mi>A</mi><mi>B</mi></mrow></semantics></math></inline-formula> level. However, considering the plausible criterion, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>+</mo><mi>A</mi><mi>B</mi></mrow></semantics></math></inline-formula> and second levels for correlations were equal, and the extremal condition in the simplest Bell scenario was replaced by that in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>+</mo><mi>A</mi><mi>B</mi></mrow></semantics></math></inline-formula> 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. |
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| ISSN: | 1099-4300 |