We investigate when the quantum correlations of a bipartite system, under the influence of environments with memory, are not reproducible with certainty by a classical local hidden variable model. For this purpose, we compare the dynamics of a Bell inequality with that of entanglement, as measured by concurrence. We find time regions when the Bell inequality is not violated even in correspondence with high values of concurrence (up to $\ensuremath{\approx}0.8$). We also suggest that these results may be observed by adopting a modification of a recent experimental optical setup. These findings indicate that even highly entangled systems cannot be exploited with certainty in contexts where the nonclassical reproducibility of quantum correlations is required.We investigate when the quantum correlations of a bipartite system, under the influence of environments with memory, are not reproducible with certainty by a classical local hidden variable model. For this purpose, we compare the dynamics of a Bell inequality with that of entanglement, as measured by concurrence. We find time regions when the Bell inequality is not violated even in correspondence with high values of concurrence (up to $\ensuremath{\approx}0.8$). We also suggest that these results may be observed by adopting a modification of a recent experimental optical setup. These findings indicate that even highly entangled systems cannot be exploited with certainty in contexts where the nonclassical reproducibility of quantum correlations is required.

arXiv:0806.3182Physical Review ADec 5, 200838 citations

Bell scenarios in which nonlocality and entanglement are inversely related

Giuseppe Vallone, G. Lima, Esteban S. Gómez +4 more

We show that for two-qubit chained Bell inequalities with an arbitrary number of measurement settings, nonlocality and entanglement are not only different properties but are inversely related. Specifically, we analytically prove that in absence of noise, robustness of nonlocality, defined as the maximum fraction of detection events that can be lost such that the remaining ones still do not admit a local model, and concurrence are inversely related for any chained Bell inequality with an arbitrary number of settings. The closer quantum states are to product states, the harder it is to reproduce quantum correlations with local models. We also show that, in presence of noise, nonlocality and entanglement are simultaneously maximized only when the noise level is equal to the maximum level tolerated by the inequality; in any other case, a more nonlocal state is always obtained by reducing the entanglement. In addition, we observed that robustness of nonlocality and concurrence are also inversely related for the Bell scenarios defined by the tight two-qubit three-setting ${I}_{3322}$ inequality, and the tight two-qutrit inequality ${I}_{3}$ .We show that for two-qubit chained Bell inequalities with an arbitrary number of measurement settings, nonlocality and entanglement are not only different properties but are inversely related. Specifically, we analytically prove that in absence of noise, robustness of nonlocality, defined as the maximum fraction of detection events that can be lost such that the remaining ones still do not admit a local model, and concurrence are inversely related for any chained Bell inequality with an arbitrary number of settings. The closer quantum states are to product states, the harder it is to reproduce quantum correlations with local models. We also show that, in presence of noise, nonlocality and entanglement are simultaneously maximized only when the noise level is equal to the maximum level tolerated by the inequality; in any other case, a more nonlocal state is always obtained by reducing the entanglement. In addition, we observed that robustness of nonlocality and concurrence are also inversely related for the Bell scenarios defined by the tight two-qubit three-setting ${I}_{3322}$ inequality, and the tight two-qutrit inequality ${I}_{3}$.

arXiv:1106.2240Physical Review AJan 3, 201415 citations

Entanglement and Bell Inequalities

Marian Kupczyński

arXiv:quant-ph/0407199Journal of Russian Laser ResearchNov 1, 200536 citations

Bell’s Inequalities and Methods of Quantifying Measures of Entanglement Correlations

Paul Bracken

International Journal of Theoretical PhysicsApr 7, 20143 citations

Bell’s inequality, generalized concurrence and entanglement in qubits

Po-Yao Chang, Su-Kuan Chu, Chen‐Te Ma

It is well known that the maximal violation of the Bell’s inequality for a two-qubit system is related to the entanglement formation in terms of a concurrence. However, a generalization of this relation to an [Formula: see text]-qubit state has not been found. In this paper, we demonstrate some extensions of the relation between the upper bound of the Bell’s violation and a generalized concurrence in several [Formula: see text]-qubit states. In particular, we show the upper bound of the Bell’s violation can be expressed as a function of the generalized concurrence, if a state can be expressed in terms of two variables. We apply the relation to the Wen-Plaquette model and show that the topological entanglement entropy can be extracted from the maximal Bell’s violation.It is well known that the maximal violation of the Bell’s inequality for a two-qubit system is related to the entanglement formation in terms of a concurrence. However, a generalization of this relation to an [Formula: see text]-qubit state has not been found. In this paper, we demonstrate some extensions of the relation between the upper bound of the Bell’s violation and a generalized concurrence in several [Formula: see text]-qubit states. In particular, we show the upper bound of the Bell’s violation can be expressed as a function of the generalized concurrence, if a state can be expressed in terms of two variables. We apply the relation to the Wen-Plaquette model and show that the topological entanglement entropy can be extracted from the maximal Bell’s violation.

arXiv:1710.10493International Journal of Modern Physics AMar 10, 20197 citations

{I}_{3322}

inequality, and the tight two-qutrit inequality

{I}_{3}