Bell inequalities resistant to detector inefficiency

Massar, Serge; Pironio, Stefano; Roland, Jérémie; Gisin, B.

doi:10.1103/physreva.66.052112

Cited by 57 publications

(72 citation statements)

References 15 publications

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“…It is worth noting that, instead of grouping inconclusive events with one of the outcomes, different strategies can be used. For instance, a further outcome, corresponding to nondetections, can be added to the observables, [15], or one can also choose to treat nondetections as simply "undefined" [16]. However, these strategies will require a modification of the Bell inequality.…”

Section: Robustness Of Nonlocalitymentioning

confidence: 99%

Bell scenarios in which nonlocality and entanglement are inversely related

et al. 2014

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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 I 3322 inequality, and the tight two-qutrit inequality I 3 .

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Section: Robustness Of Nonlocalitymentioning

confidence: 99%

Bell scenarios in which nonlocality and entanglement are inversely related

et al. 2014

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“…Other methods of constructing Bell inequalities with greater resistance to loss have been proposed in Refs. [20,[30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Fair-sampling assumption is not necessary for testing local realism

et al. 2010

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Almost all Bell inequality experiments to date have used postselection and therefore relied on the fair sampling assumption for their interpretation. The standard form of the fair sampling assumption is that the loss is independent of the measurement settings, so the ensemble of detected systems provides a fair statistical sample of the total ensemble. This is often assumed to be needed to interpret Bell inequality experiments as ruling out hidden-variable theories. Here we show that it is not necessary; the loss can depend on measurement settings, provided the detection efficiency factorizes as a function of the measurement settings and any hidden variable. This condition implies that Tsirelson's bound must be satisfied for entangled states. On the other hand, we show that it is possible for Tsirelson's bound to be violated while the Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality still holds for unentangled states, and present an experimentally feasible example.

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“…Indeed, in order to reproduce analytically the optimal numerical values of η obtained in Ref. [16] (which are identical to those given in Ref. [9]) for the case of systems of arbitrary dimension and two settings (measurements) on each side, Massar et al derived the following Bell inequality:…”

Section: Finite Detector Efficiencymentioning

confidence: 99%

“…[4] and [6] aimed to test either the inequality I 3 ≤ 2 or K 3 ≤ 0, must therefore rely on one or another sort of supplementary assumption (like the fair-sampling assumption) in order to deal with the problem of the low detection efficiencies. 11 We should add here that the threshold value in (44) was already derived in an independent way by Massar et al [16]. Indeed, in order to reproduce analytically the optimal numerical values of η obtained in Ref.…”

Section: Finite Detector Efficiencymentioning

confidence: 99%

On the Equivalence of the Ch and CHSH Inequalities for Two Three-Level Systems

Cereceda¹

2003

Int. J. Quantum Inform.

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In this paper we show a Clauser-Horne (CH) inequality for two three-level quantum systems or qutrits, alternative to the CH inequality given by Kaszlikowski et al. [Phys. Rev. A 65, 032118 (2002)]. In contrast to this latter CH inequality, the new one is shown to be equivalent to the ClauserHorne-Shimony-Holt (CHSH) inequality for two qutrits given by Collins et al. [Phys. Rev. Lett. 88, 040404 (2002)]. Both the CH and CHSH inequalities exhibit the strongest resistance to noise for a nonmaximally entangled state for the case of two von Neumann measurements per site, as first shown by Acín et al. [Phys. Rev. A 65, 052325 (2002)]. This equivalence, however, breaks down when one takes into account the less-than-perfect quantum efficiency of detectors. Indeed, for the noiseless case, the threshold quantum efficiency above which there is no local and realistic description of the experiment for the optimal choice of measurements is found to be (9 − √ 33)/4 ≈ 0.814 for the CH inequality, whereas it is equal to ( −3 + √ 33)/2 ≈ 0.828 for the CHSH inequality.

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Bell inequalities resistant to detector inefficiency

Cited by 57 publications

References 15 publications

Bell scenarios in which nonlocality and entanglement are inversely related

Bell scenarios in which nonlocality and entanglement are inversely related

Fair-sampling assumption is not necessary for testing local realism

On the Equivalence of the Ch and CHSH Inequalities for Two Three-Level Systems

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