Nonlocal multipartite correlations from local marginal probabilities

Würflinger, Lars Erik; Bancal, Jean-Daniel; Acín, Antonio; Gisin, Nicolas; Vértesi, Tamás

doi:10.1103/physreva.86.032117

Cited by 26 publications

(42 citation statements)

References 26 publications

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“…In this work we present several results that complement and generalize those of [14][15][16]. We offer a brief summary of our findings in Table I.…”

Section: Introductionsupporting

confidence: 72%

Role of correlations in the two-body-marginal problem

et al. 2014

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Quantum properties of correlations have a key role in disparate fields of physics, from quantum information processing, to quantum foundations, to strongly correlated systems. We tackle a specific aspect of the fundamental quantum marginal problem: we address the issue of deducing the global properties of correlations of tripartite quantum states based on the knowledge of their bipartite reductions, focusing on relating specific properties of bipartite correlations to global correlation properties. We prove that strictly classical bipartite correlations may still require global entanglement and that unentangled-albeit not strictly classical-reductions may require global genuine multipartite entanglement, rather than simple entanglement. On the other hand, for three qubits, the strict classicality of the bipartite reductions rules out the need for genuine multipartite entanglement. Our work sheds new light on the relation between local and global properties of quantum states, and on the interplay between classical and quantum properties of correlations.

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“…In this work we present several results that complement and generalize those of [14][15][16]. We offer a brief summary of our findings in Table I.…”

Section: Introductionsupporting

confidence: 72%

Role of correlations in the two-body-marginal problem

et al. 2014

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“…Then, it is natural to expect that Bell inequalities based on only few-body correlations are, in general, weaker in revealing nonlocality than those constructed from high-order correlations (that is, correlations among many of the observers). Whereas Bell inequalities involving correlations among all but one parties have been constructed in [49][50][51], thus proving that all-partite correlations are not necessary to reveal nonlocality, here we have to consider the more demanding question of whether nonlocality detection is possible for systems of an arbitrary number of parties from the minimal information achievable in a Bell test, i.e., two-body correlations. We answered this question positively in Ref.…”

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confidence: 99%

Nonlocality in many-body quantum systems detected with two-body correlators

et al. 2015

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Contemporary understanding of correlations in quantum many-body systems and in quantum phase transitions is based to a large extent on the recent intensive studies of entanglement in many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems, mostly because the available multipartite Bell inequalities involve high-order correlations among many particles, which are hard to access theoretically, and even harder experimentally. Standard, "theorist-and experimentalist-friendly" many-body observables involve correlations among only few (one, two, rarely three...) particles. Typically, there is no multipartite Bell inequality for this scenario based on such low-order correlations. Recently, however, we have succeeded in constructing multipartite Bell inequalities that involve two-and one-body correlations only, and showed how they revealed the nonlocality in many-body systems relevant for nuclear and atomic physics [Science 344, 1256[Science 344, (2014. With the present contribution we continue our work on this problem. On the one hand, we present a detailed derivation of the above Bell inequalities, pertaining to permutation symmetry among the involved parties. On the other hand, we present a couple of new results concerning such Bell inequalities. First, we characterize their tightness. We then discuss maximal quantum violations of these inequalities in the general case, and their scaling with the number of parties. Moreover, we provide new classes of two-body Bell inequalities which reveal nonlocality of the Dicke states-ground states of physically relevant and experimentally realizable Hamiltonians. Finally, we shortly discuss various scenarios for nonlocality detection in mesoscopic systems of trapped ions or atoms, and by atoms trapped in the vicinity of designed nanostructures.

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“…We shall use the property of monogamy of correlations [7]. Another approach has recently been put forward by Würflinger et al [8] who have shown that some non-entangled reduced density operators can be linked with global entangled states.…”

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confidence: 99%

Detecting genuine multipartite entanglement of pure states with bipartite correlations

et al. 2013

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Monogamy of bipartite correlations leads, for arbitrary pure multi-qubit states, to simple conditions able to indicate various types of multipartite entanglement by being capable to exclude the possibility of k-separability.PACS numbers: 03.67.MnFor bipartite systems the phenomenon of quantum entanglement [1, 2] manifests itself in correlations. One might expect that genuinely n-partite entanglement gives rise to non-vanishing correlations between all n subsystems. This is incorrect, at least when correlations are quantified as average values of a product of local measurement results [3,4] (for a discussion on quantum correlations without classical correlations, see e.g. [5]). Thus, in order to detect genuine multipartite entanglement of certain states one has to rely on correlations between smaller number of subsystems [6].Here we discuss global features of multiparty qubit pure states, which can be deduced from their bipartite correlations. We shall use the property of monogamy of correlations [7]. Another approach has recently been put forward by Würflinger et al. [8] who have shown that some non-entangled reduced density operators can be linked with global entangled states.Monogamy of quantum correlations can be used for entanglement detection [9]. We will use it to derive a criterion for genuine multipartite entanglement. Monogamy was also employed in studies of quantum marginal problem, i.e. conditions for existence of a global quantum state given its marginals [10], security of quantum key distribution [11], and to show that correlations between macroscopic measurements ought to be classical [12]. It leads to efficient methods of solving strongly correlated multipartite quantum lattice systems [13].States of n qubits (two-level quantum systems) have density matrices of the following form:

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Nonlocal multipartite correlations from local marginal probabilities

Cited by 26 publications

References 26 publications

Role of correlations in the two-body-marginal problem

Role of correlations in the two-body-marginal problem

Nonlocality in many-body quantum systems detected with two-body correlators

Detecting genuine multipartite entanglement of pure states with bipartite correlations

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