Bell scenarios in which nonlocality and entanglement are inversely related

Giuseppe Vallone, G. Lima, E. S. Gómez, Gustavo Cañas, Jan-Ake Larsson, P. Matalloni and A. Cabello
PHYSICAL REVIEW A 89, 12102 (2014)


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 I3322 inequality, and the tight two-qutrit inequality I3.