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Abstract: We have determined the maximum quantum violation of 241 tight bipartite Bellinequalities with up to five two-outcome measurement settings per party byconstructing the appropriate measurement operators in up to six-dimensionalcomplex and eight-dimensional real component Hilbert spaces using numericaloptimization. Out of these inequalities 129 has been introduced here. In 43cases higher dimensional component spaces gave larger violation than qubits,and in 3 occasions the maximum was achieved with six-dimensional spaces. Wehave also calculated upper bounds on these Bell inequalities using a methodproposed recently. For all but 20 inequalities the best solution found matchedthe upper bound. Surprisingly, the simplest inequality of the set examined,with only three measurement settings per party, was not among them, despite thehigh dimensionality of the Hilbert space considered. We also computed detectionthreshold efficiencies for the maximally entangled qubit pair. These could belowered in several instances if degenerate measurements were also allowed.

Author: K.F. Pál, T. Vértesi

Source: https://arxiv.org/

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