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We report correlation measurements on two $^9$Be$^+$ ions that violate a chained Bell inequality obeyed by any local-realistic theory. The correlations can be modeled as derived from a mixture of a local-realistic probabilistic distribution and a distribution that violates the inequality. A statistical framework is formulated to quantify the local-realistic fraction allowable in the observed distribution without the fair-sampling or independent-and-identical-distributions assumptions. We exclude models of our experiment whose local-realistic fraction is above 0.327 at the 95 % confidence level. This bound is significantly lower than 0.586, the minimum fraction derived from a perfect Clauser-Horne-Shimony-Holt inequality experiment. Furthermore, our data provides a device-independent certification of the deterministically created Bell states.
The correspondence principle suggests that quantum systems grow classical when large. Classical systems cannot violate Bell inequalities. Yet agents given substantial control can violate Bell inequalities proven for large-scale systems. We consider a
Quantum correlations resulting in violations of Bell inequalities have generated a lot of interest in quantum information science and fundamental physics. In this paper, we address some questions that become relevant in Bell-type tests involving syst
We observe violation of a Bell inequality between the quantum states of two remote Yb ions separated by a distance of about one meter with the detection loophole closed. The heralded entanglement of two ions is established via interference and joint
Entanglement is a critical resource used in many current quantum information schemes. As such entanglement has been extensively studied in two qubit systems and its entanglement nature has been exhibited by violations of the Bell inequality. Can the
Here we demonstrate, for the first time, violation of Bells inequality using a triggered quantum dot photon-pair source without post-selection. Furthermore, the fidelity to the expected Bell state can be increased above 90% using temporal gating to r