Nonlocality without inequality for spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>s</mml:mi></mml:math>systems

Kunkri, Samir; Choudhary, Sujit K.

doi:10.1103/physreva.72.022348

Cited by 20 publications

(31 citation statements)

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“…In order to present Hardy's argument in the general probabilistic theories, we consider the set of tripartite no-signalling correlations with binary input and binary output for each party-the set of such correlation are known to be points of a polytope in a 26dimensional space with 53, 856 extremal points [6]. A arXiv:1209.3490v1 [quant-ph] 16 Sep 2012 tripartite two-input-two-output Hardy correlation is defined by some restrictions on a certain choice of 5 out of 64 joint probabilities in the correlation matrix [12][13][14][15]. The following five conditions, for example, define a tripartite Hardy correlation:…”

Section: Tripartite Quantum Systems and Hardy Argumentmentioning

confidence: 99%

Hardy's nonlocality argument as a witness for postquantum correlations

et al. 2013

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Recently, Gallego et.al. [Phys. Rev. Lett 107, 210403 (2011)] proved that any future information principle aiming at distinguishing between quantum and post-quantum correlation must be intrinsically multipartite in nature. We establish similar result by using device independent success probability of Hardy's nonlocality argument for tripartite quantum system. We construct an example of a tri-partite Hardy correlation which is post-quantum but satisfies not only all bipartite information principle but also the GYNI inequality.

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Section: Tripartite Quantum Systems and Hardy Argumentmentioning

confidence: 99%

Hardy's nonlocality argument as a witness for postquantum correlations

et al. 2013

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“…This was observed in [5].Hardy's proof requires two observers, each with two measurements, each with two possible outcomes. The proof has been extended to the case of more than two measurements [11,12], and more than two outcomes [13][14][15]. However, none of these extensions is equivalent to the violation of a tight Bell inequality.The aim of this Letter is to show that, if we remove the requirement that the measurements have two outcomes, then Hardy's proof can be formulated in a much powerful way.…”

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confidence: 99%

Hardy's paradox for high-dimensional systems

Chen

Cabello

et al. 2013

Phys. Rev. A

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Hardy's proof is considered the simplest proof of nonlocality. Here we introduce an equally simple proof that (i) has Hardy's as a particular case, (ii) shows that the probability of nonlocal events grows with the dimension of the local systems, and (iii) is always equivalent to the violation of a tight Bell inequality.PACS numbers: 03.65. Ud, 03.67.Mn, 42.50.Xa Introduction.-Nonlocality, namely, the impossibility of describing correlations in terms of local hidden variables [1], is a fundamental property of nature. Hardy's proof [2,3], in any of its forms [4][5][6][7], provides a simple way to show that quantum correlations cannot be explained with local theories. Hardy's proof is usually considered "the simplest form of Bell's theorem" [8].On the other hand, if one wants to study nonlocality in a systematic way, one must define the local polytope [9] corresponding to any possible scenario (i.e., for any given number of parties, settings, and outcomes) and check whether quantum correlations violate the inequalities defining the facets of the corresponding local polytope. These inequalities are the so-called tight Bell inequalities. In this sense, Hardy's proof has another remarkable property: It is equivalent to a violation of a tight Bell inequality, the Clauser-Horne-ShimonyHolt (CHSH) inequality [10]. This was observed in [5].Hardy's proof requires two observers, each with two measurements, each with two possible outcomes. The proof has been extended to the case of more than two measurements [11,12], and more than two outcomes [13][14][15]. However, none of these extensions is equivalent to the violation of a tight Bell inequality.The aim of this Letter is to show that, if we remove the requirement that the measurements have two outcomes, then Hardy's proof can be formulated in a much powerful way. The new formulation shows that the maximum probability of nonlocal events, which has a limit of 0.09 in Hardy's formulation and previously proposed extensions, actually grows with the number of possible outcomes, tending asymptotically to a limit that is more than four times higher than the original one. Moreover, for any given number of outcomes, the new formulation turns out to be equivalent to a violation of a tight Bell inequality, a feature that suggest that this formulation is more fundamental than any other one proposed previously. All this while preserving the simplicity of Hardy's original proof.A new formulation of Hardy's paradox.-Let us consider two observers, Alice, who can measure either A 1 or A 2 on her subsystem, and Bob, who can measure B 1 or B 2 on his.

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“…Hence, the role of dimension played in Hardy's paradox is this: it determines which term or how many terms can be considered in the paradox. We also note that while the first type of extensions provides a minimal generalization [7] of Hardy's paradox, the second type of generalization may provide a maximal one. Our results may stimulate studies on a promising unified perspective of Hardy's paradox in fur-ther investigations.…”

Section: Discussionmentioning

confidence: 87%

“…Moreover, we further conjecture that, while the first type of extension provides a minimal generalization [7] of Hardy's paradox, the second type of extension maybe provides a maximal one.…”

Section: The Second Type Of Extensions Of Hardy's Paradoxmentioning

confidence: 77%

Dimension-independent bounds for Hardy's experiment

Chen

2014

Int. J. Quantum Inform.

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Hardy's paradox is of fundamental importance in quantum information theory. So far, there have been two types of its extensions into higher dimensions: in the first type the maximum probability of nonlocal events is roughly 9% and remains the same as the dimension changes (dimensionindependent), while in the second type the probability becomes larger as the dimension increases, reaching approximately 40% in the infinite limit. Here, we (i) give an alternative proof of the first type, (ii) study the situation in which the maximum probability of nonlocal events can also be dimension-independent in the second type, and (iii) conjecture how the situation could be changed in order that (ii) still holds.

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Nonlocality without inequality for spin-ssystems

Cited by 20 publications

References 13 publications

Hardy's nonlocality argument as a witness for postquantum correlations

Hardy's nonlocality argument as a witness for postquantum correlations

Hardy's paradox for high-dimensional systems

Dimension-independent bounds for Hardy's experiment

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