Optimal measurement bases for Bell-tests based on the CH-inequality

Abstract

The Hardy test of nonlocality can be seen as a particular case of the Bell tests based on the Clauser-Horne (CH) inequality. Here we stress this connection when we analyze the relation between the CH-inequality violation, its threshold detection efficiency, and the measurement settings adopted in the test. It is well known that the threshold efficiencies decrease when one considers partially entangled states and that the use of these states, unfortunately, generates a reduction in the CH violation. Nevertheless, these quantities are both dependent on the measurement settings considered, and in this paper we show that there are measurement bases which allow for an optimal situation in this trade-off relation. These bases are given as a generalization of the Hardy measurement bases, and they will be relevant for future Bell tests relying on pairs of entangled qubits.

8 pages, 6 figures

References in corpus (4)

• Hidden Variables and the Two Theorems of John Bell
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• Partial list of bipartite Bell inequalities with four binary settings
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Cited by in corpus (8)

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• Analysis of the Christensen et al. Clauser-Horne (CH)-Inequality-Based Test of Local Realism
• Bell tests with random measurements require very high detection efficiencies
• Detection efficiency for loophole-free Bell tests with entangled states affected by colored noise
• Chained Clauser-Horne-Shimony-Holt inequality for Hardy's ladder test of nonlocality