Bell Bi-Inequalities for Bell Local Correlation Tensors

Zhu, Wenyao; Hu, Di; Guo, Zhihua; Cao, Huaixin

doi:10.1007/s10773-023-05320-0

Cited by 3 publications

(6 citation statements)

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“…Sine ρ is Bell local, the induced CT P is Bell local. Thus, using (27) for P and = = = = a b x y 1, we get that…”

Section: A X B Ymentioning

confidence: 99%

“…Thus, the Hardy-Bell inequality (27) is more useful than the Hardy paradox (26) and the CHSH inequality (48). Actually, the CHSH inequality (48) can be deduced from the Hardy-Bell inequalities (27). To check this, we assume that (27) are valid for all a, b, x, y = 0, 1.…”

Section: A X B Ymentioning

confidence: 99%

“…Actually, the CHSH inequality (48) can be deduced from the Hardy-Bell inequalities (27). To check this, we assume that (27) are valid for all a, b, x, y = 0, 1. First, (48) can be written as…”

Section: A X B Ymentioning

confidence: 99%

“…see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]). Typically, the verification of Bell nonlocality involves two main approaches: the violation of specific Bell inequalities [16][17][18][19][20][21][22][23][24][25][26][27], and the utilization of the no-inequality methods or all-versusnothing (AVN) proof. Notable examples within the AVN proof include the Hardy paradox [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] and the arguments presented by GHZ [45][46][47]53].…”

Section: Introductionmentioning

confidence: 99%

“…-known to be Bell nonlocal. In light of matrix representation(44), it was proved in[27] that a CT P = §P(a, b|x, y)¨over D¢ 2 is Bell if and only if it can be written as…”

mentioning

confidence: 99%

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Hardy-Bell inequalities and fault-tolerant Hardy paradoxes

Han,

Zhu,

Guo

et al. 2023

Phys. Scr.

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Usually, the verification of Bell nonlocality involves two main approaches: violation of specific inequalities and utilization of no-inequality methods. In this paper, we continue to develop the inequality methods by deducing the so-called ‘Hardy-Bell inequalities (HBIs)’ and ‘fault-tolerant Hardy paradoxes (FTHPs)’ for correlation tensors (CTs) with two inputs and general outcomes. We prove that the HBIs are necessary conditions for a CT to be Bell local and one of the FTHPs is sufficient condition for a CT to be Bell nonlocal. We demonstrate the effectiveness of HBIs in determining the nonlocality of CTs or quantum states when the classical Hardy paradox does not appear or a Bell inequality is not violated. Consequently, our methods can be utilized to explore more correlations having Bell nonlocality. Based on the obtained results, we find a neighborhood of a Hardy nonlocal state, in which all states are all Bell nonlocal.

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“…Sine ρ is Bell local, the induced CT P is Bell local. Thus, using (27) for P and = = = = a b x y 1, we get that…”

Section: A X B Ymentioning

confidence: 99%

Section: A X B Ymentioning

confidence: 99%

Section: A X B Ymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…-known to be Bell nonlocal. In light of matrix representation(44), it was proved in[27] that a CT P = §P(a, b|x, y)¨over D¢ 2 is Bell if and only if it can be written as…”

mentioning

confidence: 99%

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