Towards an equivalence between maximal entanglement and maximal quantum nonlocality
While all bipartite pure entangled states are known to generate correlations violating a Bell inequality, and are therefore nonlocal, the quantitative relation between pure state entanglement and nonlocality is poorly understood. In fact, some Bell inequalities are maximally violated by non-maximall...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2018-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/aaca22 |
| _version_ | 1827873334150299648 |
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| author | Victoria Lipinska Florian J. Curchod Alejandro Máttar Antonio Acín |
| author_facet | Victoria Lipinska Florian J. Curchod Alejandro Máttar Antonio Acín |
| author_sort | Victoria Lipinska |
| collection | DOAJ |
| description | While all bipartite pure entangled states are known to generate correlations violating a Bell inequality, and are therefore nonlocal, the quantitative relation between pure state entanglement and nonlocality is poorly understood. In fact, some Bell inequalities are maximally violated by non-maximally entangled states and this phenomenon is also observed for other operational measures of nonlocality. In this work, we study a recently proposed measure of nonlocality defined as the probability that a pure state displays nonlocal correlations when subjected to random measurements. We first prove that this measure satisfies some natural properties for an operational measure of nonlocality. Then, we show that for pure states of two qubits the measure is monotonic with entanglement for all correlation two-outcome Bell inequalities: for all these inequalities, the more the state is entangled, the larger the probability to violate them when random measurements are performed. Finally, we extend our results to the multipartite setting. |
| first_indexed | 2024-03-12T16:36:38Z |
| format | Article |
| id | doaj.art-a1350949aaa2440392a7d934b5b5e9b5 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:36:38Z |
| publishDate | 2018-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-a1350949aaa2440392a7d934b5b5e9b52023-08-08T14:52:43ZengIOP PublishingNew Journal of Physics1367-26302018-01-0120606304310.1088/1367-2630/aaca22Towards an equivalence between maximal entanglement and maximal quantum nonlocalityVictoria Lipinska0Florian J. Curchod1Alejandro Máttar2Antonio Acín3QuTech, Delft University of Technology , Lorentzweg 1, 2628 CJ Delft, The Netherlands; ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology , E-08860 Castelldefels (Barcelona), SpainICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology , E-08860 Castelldefels (Barcelona), SpainICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology , E-08860 Castelldefels (Barcelona), SpainICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology , E-08860 Castelldefels (Barcelona), Spain; ICREA-Institució Catalana de Recerca i Estudis Avançats , Lluis Companys 23, E-08010 Barcelona, SpainWhile all bipartite pure entangled states are known to generate correlations violating a Bell inequality, and are therefore nonlocal, the quantitative relation between pure state entanglement and nonlocality is poorly understood. In fact, some Bell inequalities are maximally violated by non-maximally entangled states and this phenomenon is also observed for other operational measures of nonlocality. In this work, we study a recently proposed measure of nonlocality defined as the probability that a pure state displays nonlocal correlations when subjected to random measurements. We first prove that this measure satisfies some natural properties for an operational measure of nonlocality. Then, we show that for pure states of two qubits the measure is monotonic with entanglement for all correlation two-outcome Bell inequalities: for all these inequalities, the more the state is entangled, the larger the probability to violate them when random measurements are performed. Finally, we extend our results to the multipartite setting.https://doi.org/10.1088/1367-2630/aaca22quantum nonlocalityquantum correlationsentanglemententanglement anomalynonlocality measurenonlocal volume |
| spellingShingle | Victoria Lipinska Florian J. Curchod Alejandro Máttar Antonio Acín Towards an equivalence between maximal entanglement and maximal quantum nonlocality New Journal of Physics quantum nonlocality quantum correlations entanglement entanglement anomaly nonlocality measure nonlocal volume |
| title | Towards an equivalence between maximal entanglement and maximal quantum nonlocality |
| title_full | Towards an equivalence between maximal entanglement and maximal quantum nonlocality |
| title_fullStr | Towards an equivalence between maximal entanglement and maximal quantum nonlocality |
| title_full_unstemmed | Towards an equivalence between maximal entanglement and maximal quantum nonlocality |
| title_short | Towards an equivalence between maximal entanglement and maximal quantum nonlocality |
| title_sort | towards an equivalence between maximal entanglement and maximal quantum nonlocality |
| topic | quantum nonlocality quantum correlations entanglement entanglement anomaly nonlocality measure nonlocal volume |
| url | https://doi.org/10.1088/1367-2630/aaca22 |
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