Hardy’s approach, Eberhard’s inequality, and supplementary assumptions

Garuccio, Augusto

doi:10.1103/physreva.52.2535

Cited by 48 publications

(50 citation statements)

References 6 publications

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“…At any fixed proper time τ , the derivation of (3.4) follows the one in [26] for the timeindependent case. However, the same class of inequalities can be deduced from the larger class of Bell's like inequalities which has been obtained in [10] via an argument which essentially adapts the derivation of Wigner, Belinfante and Holt (see [20], section 3.7).…”

Section: Bell-like Inequalities With Neutral Kaonsmentioning

confidence: 88%

Direct CP-violation as a test of quantum mechanics

Benatti

Floreanini

2000

Eur. Phys. J. C

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Section: Bell-like Inequalities With Neutral Kaonsmentioning

confidence: 88%

Direct CP-violation as a test of quantum mechanics

Benatti

Floreanini

2000

Eur. Phys. J. C

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“…These probabilities can be modified to include the detection efficiency, η, defined as the ratio between the number of detected events and the number of prepared systems. For this reason, it is always possible to rewrite Bell inequalities in terms of η [23,36]. The modified Bell inequality can only be violated when the detection efficiency value overcomes a certain critical value, the socalled threshold detection efficiency, η crit [37].…”

Section: Threshold Detection Efficienciesmentioning

confidence: 99%

“…Following the method of [23,36] and considering a symmetric Bell test (i.e., η = η A = η B ), we can rewrite the I CH3 inequality as…”

Section: Threshold Detection Efficienciesmentioning

confidence: 99%

Higher quantum bound for the Vértesi-Bene-Bell inequality and the role of positive operator-valued measures regarding its threshold detection efficiency

et al. 2012

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Recently, Vértesi and Bene [Phys. Rev. A. 82, 062115 (2010)] derived a two-qubit Bell inequality, ICH3, which they show to be maximally violated only when more general positive operator valued measures (POVMs) are used instead of the usual von Neumann measurements. Here we consider a general parametrization for the three-element-POVM involved in the Bell test and obtain a higher quantum bound for the ICH3-inequality. With a higher quantum bound for ICH3, we investigate if there is an experimental setup that can be used for observing that POVMs give higher violations in Bell tests based on this inequality. We analyze the maximum errors supported by the inequality to identify a source of entangled photons that can be used for the test. Then, we study if POVMs are also relevant in the more realistic case that partially entangled states are used in the experiment. Finally, we investigate which are the required efficiencies of the ICH3-inequality, and the type of measurements involved, for closing the detection loophole. We obtain that POVMs allow for the lowest threshold detection efficiency, and that it is comparable to the minimal (in the case of twoqubits) required detection efficiency of the Clauser-Horne-Bell-inequality.

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“…This inequality is equivalent to the Clauser-Horne (CH) inequality [9,10]. The quantum violation of the CH inequality is the difference between the value of P (φ 2 ,φ 3 ) predicted by quantum mechanics and the value given by the sum of the probabilities on the right-hand side of Eq.…”

Section: Introductionmentioning

confidence: 99%

“…As it was discussed by Mermin and Garuccio in [4,9], Hardy's test can be generalized when it is written in terms of the following inequality: P (φ 2 ,φ 3 ) P (φ 1 ,φ 3 ) + P (φ 1 ,φ 4 ) + P (φ 2 ,φ 4 …”

Section: Introductionmentioning

confidence: 99%

Optimal measurement bases for Bell tests based on the Clauser-Horne inequality

et al. 2012

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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.

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Hardy’s approach, Eberhard’s inequality, and supplementary assumptions

Cited by 48 publications

References 6 publications

Direct CP-violation as a test of quantum mechanics

Direct CP-violation as a test of quantum mechanics

Higher quantum bound for the Vértesi-Bene-Bell inequality and the role of positive operator-valued measures regarding its threshold detection efficiency

Optimal measurement bases for Bell tests based on the Clauser-Horne inequality

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