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Minimum Detection Efficiencies for a Loophole-Free Bell-type Test

We discuss the problem of finding the most favorable conditions for closing the detection loophole in a test of local realism with a Bell inequality. For a generic non-maximally entangled two-qubit state and two alternative measurement bases we apply Hardy's proof of non-locality without inequality and derive an Eberhard-like inequality. For an infinity of non-maximally entangled states we find that it is possible to refute local realism by requiring perfect detection efficiency for only one of the two measurements: the test is free from the detection loophole for any value of the detection efficiency corresponding to the other measurement. The maximum tolerable noise in a loophole-free test is also evaluated.

preprint2009arXivOpen access
G. Garbarino
hep-phquant-ph
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G. Garbarino

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