Broken Arrows: Hardy–Unruh Chains and Quantum Contextuality
Hardy and Unruh constructed a family of non-maximally entangled states of pairs of particles giving rise to correlations that cannot be accounted for with a local hidden-variable theory. Rather than pointing to violations of some Bell inequality, however, they pointed to apparent clashes with the ba...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/12/1568 |
| _version_ | 1827574862031355904 |
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| author | Michael Janas Michel Janssen |
| author_facet | Michael Janas Michel Janssen |
| author_sort | Michael Janas |
| collection | DOAJ |
| description | Hardy and Unruh constructed a family of non-maximally entangled states of pairs of particles giving rise to correlations that cannot be accounted for with a local hidden-variable theory. Rather than pointing to violations of some Bell inequality, however, they pointed to apparent clashes with the basic rules of logic. Specifically, they constructed these states and the associated measurement settings in such a way that the outcomes satisfy some conditionals but not an additional one entailed by them. Quantum mechanics avoids the broken ‘if …then …’ arrows in such Hardy–Unruh chains, as we call them, because it cannot simultaneously assign truth values to all conditionals involved. Measurements to determine the truth value of some preclude measurements to determine the truth value of others. Hardy–Unruh chains thus nicely illustrate quantum contextuality: which variables do and do not obtain definite values depends on what measurements we decide to perform. Using a framework inspired by Bub and Pitowsky and developed in our book <i>Understanding Quantum Raffles</i> (co-authored with Michael E. Cuffaro), we construct and analyze Hardy–Unruh chains in terms of fictitious bananas mimicking the behavior of spin-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfrac><mn>1</mn><mn>2</mn></mfrac></semantics></math></inline-formula> particles. |
| first_indexed | 2024-03-08T20:48:04Z |
| format | Article |
| id | doaj.art-c35ec917bf814bc2adf2004f17b672e2 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-08T20:48:04Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-c35ec917bf814bc2adf2004f17b672e22023-12-22T14:07:12ZengMDPI AGEntropy1099-43002023-11-012512156810.3390/e25121568Broken Arrows: Hardy–Unruh Chains and Quantum ContextualityMichael Janas0Michel Janssen1School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USASchool of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USAHardy and Unruh constructed a family of non-maximally entangled states of pairs of particles giving rise to correlations that cannot be accounted for with a local hidden-variable theory. Rather than pointing to violations of some Bell inequality, however, they pointed to apparent clashes with the basic rules of logic. Specifically, they constructed these states and the associated measurement settings in such a way that the outcomes satisfy some conditionals but not an additional one entailed by them. Quantum mechanics avoids the broken ‘if …then …’ arrows in such Hardy–Unruh chains, as we call them, because it cannot simultaneously assign truth values to all conditionals involved. Measurements to determine the truth value of some preclude measurements to determine the truth value of others. Hardy–Unruh chains thus nicely illustrate quantum contextuality: which variables do and do not obtain definite values depends on what measurements we decide to perform. Using a framework inspired by Bub and Pitowsky and developed in our book <i>Understanding Quantum Raffles</i> (co-authored with Michael E. Cuffaro), we construct and analyze Hardy–Unruh chains in terms of fictitious bananas mimicking the behavior of spin-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfrac><mn>1</mn><mn>2</mn></mfrac></semantics></math></inline-formula> particles.https://www.mdpi.com/1099-4300/25/12/1568Hardy paradoxquantum contextualitycorrelation polytopesBell inequalities |
| spellingShingle | Michael Janas Michel Janssen Broken Arrows: Hardy–Unruh Chains and Quantum Contextuality Entropy Hardy paradox quantum contextuality correlation polytopes Bell inequalities |
| title | Broken Arrows: Hardy–Unruh Chains and Quantum Contextuality |
| title_full | Broken Arrows: Hardy–Unruh Chains and Quantum Contextuality |
| title_fullStr | Broken Arrows: Hardy–Unruh Chains and Quantum Contextuality |
| title_full_unstemmed | Broken Arrows: Hardy–Unruh Chains and Quantum Contextuality |
| title_short | Broken Arrows: Hardy–Unruh Chains and Quantum Contextuality |
| title_sort | broken arrows hardy unruh chains and quantum contextuality |
| topic | Hardy paradox quantum contextuality correlation polytopes Bell inequalities |
| url | https://www.mdpi.com/1099-4300/25/12/1568 |
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