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**Towards an equivalence between maximal entanglement and maximal quantum nonlocality.** / Lipinska, Victoria; Curchod, Florian J.; Máttar, Alejandro; Acín, Antonio.

Research output: Contribution to journal › Article › Scientific › peer-review

Lipinska, V, Curchod, FJ, Máttar, A & Acín, A 2018, 'Towards an equivalence between maximal entanglement and maximal quantum nonlocality' *New Journal of Physics*, vol. 20, no. 6, 063043. https://doi.org/10.1088/1367-2630/aaca22

Lipinska, V., Curchod, F. J., Máttar, A., & Acín, A. (2018). Towards an equivalence between maximal entanglement and maximal quantum nonlocality. *New Journal of Physics*, *20*(6), [063043]. https://doi.org/10.1088/1367-2630/aaca22

Lipinska V, Curchod FJ, Máttar A, Acín A. Towards an equivalence between maximal entanglement and maximal quantum nonlocality. New Journal of Physics. 2018 Jun 1;20(6). 063043. https://doi.org/10.1088/1367-2630/aaca22

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title = "Towards an equivalence between maximal entanglement and maximal quantum nonlocality",

abstract = "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.",

keywords = "entanglement, entanglement anomaly, nonlocal volume, nonlocality measure, quantum correlations, quantum nonlocality",

author = "Victoria Lipinska and Curchod, {Florian J.} and Alejandro M{\'a}ttar and Antonio Ac{\'i}n",

year = "2018",

month = "6",

day = "1",

doi = "10.1088/1367-2630/aaca22",

language = "English",

volume = "20",

journal = "New Journal of Physics",

issn = "1367-2630",

publisher = "IOP Publishing",

number = "6",

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TY - JOUR

T1 - Towards an equivalence between maximal entanglement and maximal quantum nonlocality

AU - Lipinska, Victoria

AU - Curchod, Florian J.

AU - Máttar, Alejandro

AU - Acín, Antonio

PY - 2018/6/1

Y1 - 2018/6/1

N2 - 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.

AB - 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.

KW - entanglement

KW - entanglement anomaly

KW - nonlocal volume

KW - nonlocality measure

KW - quantum correlations

KW - quantum nonlocality

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U2 - 10.1088/1367-2630/aaca22

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T2 - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

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