All Entangled Pure States Violate a Single Bell’s Inequality

Yu, Sixia; Chen, Qing; Zhang, Chengjie; Lai, Ching-Yi; Oh, C. H.

doi:10.1103/physrevlett.109.120402

Cited by 94 publications

(84 citation statements)

References 19 publications

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“…We note that our result above strengthens previous works [21,22] in two folds. On the one hand all pure multipartite entangled symmetric states are proved to exhibit genuine multipartite nonlocality and on the other hand, this nonlocality can be revealed by a test without inequality.…”

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confidence: 92%

“…Discussions.-All pure entangled states exhibit standard nonlocality [21,23] and it is an open problem whether all pure genuine multipartite entangled states are genuine multipartite nonlocal [2]. We have made a progress towards solving this problem by proposing a test without inequality, with the help of which we have shown that all entangled symmetric states are genuine multipartite nonlocal.…”

mentioning

confidence: 99%

“…Thus without loss of generality, we suppose that |0 I is already the closest product state of |ψ . The computational basis determined by the closest product state is a magic basis [21] in which h 0 = 0 and h 1 = 0. All entangled symmetric states have been proved to exhibit 'standard' nonlocality [22].…”

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confidence: 99%

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Test of Genuine Multipartite Nonlocality without Inequalities

Chen

Zhang

et al. 2014

Phys. Rev. Lett.

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In this letter we propose a set of conditions on the joint probabilities as a test of genuine multipartite nonlocality without inequality. Our test is failed by all non-signaling local models in which even nonlocal correlations among some observables (not all) are allowed as long as these correlations respect the non-signaling principle. A pass of our test by a state therefore indicates that this state cannot be simulated by any non-signaling local models, i.e., the state exhibits genuine multipartite nonlocality. It turns out that all entangled symmetric n-qubit (n ≥ 3) states pass our test and therefore are n-way nonlocal. Also we construct two Bell-type inequalities from our proposed test whose violations indicate genuine multipartite nonlocal correlations.Introduction.-Local measurements performed on composite quantum system can lead to correlations incompatible with local hidden variable theory [1]. This phenomenon is known as quantum nonlocality, which has been recognized as an essential resource for quantum information tasks [2], such as quantum key distribution [3], communication complexity [4], and randomness generation [5]. Quantum nonlocality can be revealed via several ingenious ways such as the violations of various Bell inequalities [1,6], GHZ paradoxes [7,8], a kind of all-versus-nothing tests, and Hardy's test of nonlocality without inequality [9,10], a kind of all-versus-something tests. Most of these tests are designed to rule out 'standard' local realistic models, i.e., in the case of multipartite system each observer cannot have nonlocal correlations with any other distant observers.However, similar to the case of quantum entanglement, quantum nonlocality displays a much richer and more complex structure for the multipartite case than the bipartite case. In the case of three or more observers it is possible to have a hybrid local/nonlocal model in which some observers may share some nonlocal correlations. Still there are quantum correlations that cannot be explained by these more general local models and therefore these states exhibit genuine multipartite or n-way nonlocality [11]. Genuine multipartite nonlocality, being the strongest form of multipartite nonlocality in which nonlocal correlations are established among all the parties of the system, naturally attracts much interest recently. The detection of genuine multipartite nonlocality also witnesses genuine multipartite entanglement in a device-independent way.Svetlichny [11] introduced the notion of genuine multipartite nonlocality for the first time and provided a Bell-type inequality to detect genuine tripartite nonlocality. Recently the result was generalized to arbitrary partite cases [12] and arbitrary dimensions [13]. However Svetlichny's notion of genuine nonlocality is so general that correlations capable of two-way signaling are allowed

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confidence: 92%

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Test of Genuine Multipartite Nonlocality without Inequalities

Chen

Zhang

et al. 2014

Phys. Rev. Lett.

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“…If this new Majorana point is not one of the Majorana points of |ψ , condition (6) is satisfied automatically. It has been proven [6] that for all symmetric states except Dicke states, there exists a choice of |η i such that (6) to (8) are all satisfied, which also violates (9). Although Dicke states do not satisfy (6) to (8), it is also possible to choose measurement settings such that they violate (9) in a 2-setting/2-outcome experiment [6].…”

Section: N-party Hardy Paradox and Inequalitymentioning

confidence: 99%

“…Although Dicke states do not satisfy (6) to (8), it is also possible to choose measurement settings such that they violate (9) in a 2-setting/2-outcome experiment [6]. Indeed, is has recently been shown that all pure entangled states violate (9) [9].…”

Section: N-party Hardy Paradox and Inequalitymentioning

confidence: 99%