Multicomponent Bell inequality and its violation for continuous-variable systems

Chen, Jing-Ling; Wu, Chunfeng; Kwek, Leong Chuan; Kaszlikowski, Dagomir; Żukowski, Marek; Oh, C. H.

doi:10.1103/physreva.71.032107

Cited by 10 publications

(7 citation statements)

References 25 publications

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“…Apart from the CGLMP inequalities, there are only a few other classes of Bell inequalities that are specifically catered for multiple outcomes. Some of these are defined in terms of joint and marginal probabilities of experimental outcomes [15,29,30,31,32,33,34], whereas the others [35,36,37,38,39] are defined in terms of correlation functions -i.e., expectation value of the product of experimental outcomes. In general, however, very little is known about the tightness of these inequalities [15,32,33,34,40].…”

Section: Introductionmentioning

confidence: 99%

Reexamination of a multisetting Bell inequality for qudits

Liang¹,

Lim

Deng

2009

Phys. Rev. A

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The class of d-setting, d-outcome Bell inequalities proposed by Ji and collaborators [Phys. Rev. A 78, 052103] are reexamined. For every positive integer d > 2, we show that the corresponding non-trivial Bell inequality for probabilities provides the maximum classical winning probability of the Clauser-Horne-Shimony-Holt-like game with d inputs and d outputs. We also demonstrate that the general classical upper bounds given by Ji et al. are underestimated, which invalidates many of the corresponding correlation inequalities presented thereof. We remedy this problem, partially, by providing the actual classical upper bound for d less than or equal to 13 (including non-prime values of d). We further determine that for prime value d in this range, most of these probability and correlation inequalities are tight, i.e., facet-inducing for the respective classical correlation polytope. Stronger lower and upper bounds on the quantum violation of these inequalities are obtained. In particular, we prove that once the probability inequalities are given, their correlation counterparts given by Ji and co-workers are no longer relevant in terms of detecting the entanglement of a quantum state.Comment: v3: Published version (minor rewordings, typos corrected, upper bounds in Table III improved/corrected); v2: 7 pages, 1 figure, 4 tables (substantially revised with new results on the tightness of the correlation inequalities included); v1: 7.5 pages, 1 figure, 4 tables (Comments are welcome

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Section: Introductionmentioning

confidence: 99%

Reexamination of a multisetting Bell inequality for qudits

Liang¹,

Lim

Deng

2009

Phys. Rev. A

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“…Moreover, maximal violations of the EPR state by multicomponent Bell's inequalities have also been investigated in Refs. [15,16].…”

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confidence: 99%

“…However, attempt has also been made to reveal its nonlocality in phase space by considering displaced parity operators upon the NOPA state in the large r limit 10 . Moreover, maximal violations of the EPR state by multicomponent Bell’s inequalities have also been investigated in refs 15 , 16 .…”

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confidence: 99%

Sharp Contradiction for Local-Hidden-State Model in Quantum Steering

Chen

et al. 2016

Sci Rep

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In quantum theory, no-go theorems are important as they rule out the existence of a particular physical model under consideration. For instance, the Greenberger-Horne-Zeilinger (GHZ) theorem serves as a no-go theorem for the nonexistence of local hidden variable models by presenting a full contradiction for the multipartite GHZ states. However, the elegant GHZ argument for Bell’s nonlocality does not go through for bipartite Einstein-Podolsky-Rosen (EPR) state. Recent study on quantum nonlocality has shown that the more precise description of EPR’s original scenario is “steering”, i.e., the nonexistence of local hidden state models. Here, we present a simple GHZ-like contradiction for any bipartite pure entangled state, thus proving a no-go theorem for the nonexistence of local hidden state models in the EPR paradox. This also indicates that the very simple steering paradox presented here is indeed the closest form to the original spirit of the EPR paradox.

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“…[7]. Such an inequality is later modified into more compact forms [8,9] and its numerical violations for high-dimensional situations have also been investigated in [10,11].…”

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confidence: 99%

Maximal Quantum Violation of the CGLMP Inequality on Its Both Sides

Deng

Chen

2008

Int. J. Quantum Inform.

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We investigate the maximal violations for both sides of the d-dimensional CGLMP inequality by using the Bell operator method. It turns out that the maximal violations have a decelerating increase as the dimension increases and tend to a finite value at infinity. The numerical values are given out up to d = 10 6 for positively maximal violations and d = 2 × 10 5 for negatively maximal violations. Counterintuitively, the negatively maximal violations tend to be a little stronger than the positively maximal violations. Further we show the states corresponding to these maximal violations and compare them with the maximally entangled states by utilizing entangled degree defined by von Neumann entropy. It shows that their entangled degree tends to some nonmaximal value as the dimension increases.Bell inequality [1], arising from the Einstein-Podolsky-Rosen (EPR) paradox [2], has developed into an effective criterion between the classical and quantum theory. The famous Clauser-Horne-Shimony-Holt (CHSH) inequality[3] for two entangled spin-1/2 particles has always provided an excellent test-bed for experimental verification of quantum mechanics against the predictions of local realism. In 2002, two research teams independently developed Bell inequalities for high-dimensional systems: the first one is a Clauser-Horne type (probability) inequality for two qutrits [4,5]; the second one is a CHSH type inequality for two qudits (d is an arbitrarily high dimension), now known as the Collins-Gisin-Linden-Masser-Popoescu (CGLMP) inequality [6]. The tightness of the CGLMP inequality was * Electronic address: chenjl@nankai.edu.cn

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Multicomponent Bell inequality and its violation for continuous-variable systems

Cited by 10 publications

References 25 publications

Reexamination of a multisetting Bell inequality for qudits

Reexamination of a multisetting Bell inequality for qudits

Sharp Contradiction for Local-Hidden-State Model in Quantum Steering

Maximal Quantum Violation of the CGLMP Inequality on Its Both Sides

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