Information-causality and extremal tripartite correlations

Yang, Tzyh Haur; Cavalcanti, Daniel; Almeida, Mafalda L.; Teo, Colin; Scarani, Valerio

doi:10.1088/1367-2630/14/1/013061

Cited by 32 publications

(40 citation statements)

References 20 publications

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“…For instance, the correlations provided in [7] violate GYNI and, consequently, also LO, but satisfy every bipartite principle. Also box number 4 in [29] is an example of a tripartite no-signaling box which cannot be ruled out by any bipartite principle [30], but which violates LO.…”

Section: Resultsmentioning

confidence: 99%

Local orthogonality as a multipartite principle for quantum correlations

et al. 2013

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In recent years, the use of information principles to understand quantum correlations has been very successful. Unfortunately, all principles considered so far have a bipartite formulation, but intrinsically multipartite principles, yet to be discovered, are necessary for reproducing quantum correlations. Here we introduce local orthogonality, an intrinsically multipartite principle stating that events involving different outcomes of the same local measurement must be exclusive or orthogonal. We prove that it is equivalent to no-signalling in the bipartite scenario but more restrictive for more than two parties. By exploiting this nonequivalence, it is then demonstrated that some bipartite supra-quantum correlations do violate the local orthogonality when distributed among several parties. Finally, we show how its multipartite character allows revealing the non-quantumness of correlations for which any bipartite principle fails. We believe that local orthogonality is a crucial ingredient for understanding no-signalling and quantum correlations.

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Section: Resultsmentioning

confidence: 99%

Local orthogonality as a multipartite principle for quantum correlations

et al. 2013

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“…The intrinsically multipartite character of the LO principle has allowed us to witness the supra-quantumness of box number 4 in [39], which cannot be achieved with any bipartite principle [40]. One example of an LO inequality in the (6, 2, 2) scenario which is violated by two copies of this box is given by…”

Section: Lo ∞ and Supra-quantum Tripartite Boxesmentioning

confidence: 99%

Exploring the local orthogonality principle

et al. 2014

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Nonlocality is arguably one of the most fundamental and counterintuitive aspects of quantum theory. Nonlocal correlations could, however, be even more nonlocal than quantum theory allows, while still complying with basic physical principles such as no-signaling. So why is quantum mechanics not as nonlocal as it could be? Are there other physical or information-theoretic principles which prohibit this? So far, the proposed answers to this question have been only partially successful, partly because they are lacking genuinely multipartite formulations. In [1], we have introduced the principle of Local Orthogonality (LO), an intrinsically multipartite principle which is satisfied by quantum mechanics but is violated by non-physical correlations.Here we further explore the LO principle, presenting additional results and explaining some of its subtleties. In particular, we show that the set of no-signaling boxes satisfying LO is closed under wirings, present a classification of all LO inequalities in certain scenarios, show that all extremal tripartite boxes with two binary measurements per party violate LO, and explain the connection between LO inequalities and unextendible product bases.

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“…It has been shown that, some general physical principles can restrict the set of nosignalling correlations among distant observers to a significant degree. Information theoretic principles like information causality [1] and nontrivial communication complexity [2,3] are novel proposals to single out the quantum correlations, from rest of the no-signalling correlations, when two distant observers (or in some cases even when more than two observers [5]) are involved. However, by applying the known information principles to the bipartite case, it has not been possible to derive the full set of quantum correlations resulting from the Hilbert space structure of quantum mechanics.…”

Section: Introductionmentioning

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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Information-causality and extremal tripartite correlations

Cited by 32 publications

References 20 publications

Local orthogonality as a multipartite principle for quantum correlations

Local orthogonality as a multipartite principle for quantum correlations

Exploring the local orthogonality principle

Hardy's nonlocality argument as a witness for postquantum correlations

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