Definitions of multipartite nonlocality

Bancal, Jean-Daniel; Barrett, Jonathan; Gisin, Nicolas; Pironio, Stefano

doi:10.1103/physreva.88.014102

Cited by 197 publications

(366 citation statements)

References 28 publications

Supporting

Mentioning

349

Contrasting

Order By: Relevance

“…In recent years, nonlocality has come to be appreciated as an operational resource [9], which plays an essential role, e.g., for the implementation of secure quantum key distribution [10]. The concept of multipartite nonlocality is, however, significantly less understood than its bipartite counterpart [3][4][5]9,[11][12][13][14][15][16][17]. For a tripartite system, the conventionally employed inequality, whose violation signals a genuine three-way nonlocality, is due to Svetlichny [12].…”

mentioning

confidence: 99%

Theory of Genuine Tripartite Nonlocality of Gaussian States

Adesso

Piano

2014

Phys. Rev. Lett.

View full text Add to dashboard Cite

We investigate the genuine multipartite nonlocality of three-mode Gaussian states of continuous variable systems. For pure states, we present a simplified procedure to obtain the maximum violation of the Svetlichny inequality based on displaced parity measurements, and we analyze its interplay with genuine tripartite entanglement measured via Rényi-2 entropy. The maximum Svetlichny violation admits tight upper and lower bounds at fixed tripartite entanglement. For mixed states, no violation is possible when the purity falls below 0.86. We also explore a set of recently derived weaker inequalities for three-way nonlocality, finding violations for all tested pure states. Our results provide a strong signature for the nonclassical and nonlocal nature of Gaussian states despite their positive Wigner function, and lead to precise recipes for its experimental verification.

show abstract

mentioning

confidence: 99%

Theory of Genuine Tripartite Nonlocality of Gaussian States

Adesso

Piano

2014

Phys. Rev. Lett.

View full text Add to dashboard Cite

show abstract

“…Correlations exceeding the bound reveal the failure of local realism, that is, the presence of nonlocality. We refer the reader to [1,4,6,18,19] and references therein for an updated account on the subject.…”

Section: Svetlichny Inequalitymentioning

confidence: 99%

“…More recent studies have led to the identification of a larger set of weaker inequalities, whose violation (even without a violation of Svetlichny inequality) is still sufficient to demonstrate genuine multipartite nonlocality [18,19]. Analysing these weaker yet more complex inequalities is considerably more cumbersome in continuous variable systems, and furthermore it is not clear a priori which inequalities can be violated on specific classes of states (and in some cases what is their maximum possible quantum violation), even though the violation of one such inequality has been investigated theoretically for three-mode Gaussian states using displaced parity measurements in [36].…”

Section: Maximum Tripartite Nonlocality With Pseudospin Measurementsmentioning

confidence: 99%

“…Such an inequality can be violated e.g. by both Greenberger-Horne-Zeilinger (GHZ) and W classes of states for three qubits [15,16], and it stands as the conventional witness of genuine nonlocality when all three parties perform two measurements with two outcomes each [19], even though a large number of weaker inequalities revealing genuine nonlocality in more general settings have been constructed more recently [18,19]. While originally formulated for dichotomic observables, Bell-type inequalities such as the Svetlichny one can be tested for continuous variable systems either by binning outcomes of observables with continuous spectrum (typically Gaussianity-preserving measurements such as homodyne detection) [25,26], or by considering directly operators with a discrete spectrum [27,30].…”

Section: Introductionmentioning

confidence: 99%

“…While a great deal of attention has been devoted to the study of Bell inequalities in bipartite systems [1,3,4,6,7], including most recently the first loopholefree experimental demonstrations [8][9][10], a few criteria have been formulated for the verification of Bell nonlocality in multipartite systems as well [1,[11][12][13][14][15][16][17][18][19]. However, the concept of genuine multipartite nonlocality has been formalized only recently from an operational point of view [18,19] and its full exploration remains challenging both theoretically and experimentally.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Genuine multipartite nonlocality of permutationally invariant Gaussian states

Tufarelli

Adesso

2017

Phys. Rev. A

View full text Add to dashboard Cite

We investigate genuine multipartite nonlocality of pure permutationally invariant multimode Gaussian states of continuous variable systems, as detected by the violation of Svetlichny inequality. We identify the phase space settings leading to the largest violation of the inequality when using displaced parity measurements, distinguishing our results between the cases of even and odd total number of modes. We further consider pseudospin measurements and show that, for three-mode states with asymptotically large squeezing degree, particular settings of these measurements allow one to approach the maximum violation of Svetlichny inequality allowed by quantum mechanics. This indicates that the strongest manifestation of genuine multipartite quantum nonlocality is in principle verifiable on Gaussian states.

show abstract

More nonlocality with less entanglement in a tripartite atom‐optomechanical system

Zhang

Xuereb

et al. 2014

Annalen der Physik

View full text Add to dashboard Cite

We study quantum effects in hybrid atomic optomechanics in a system comprising a cloud of atoms and a mobile mirror mediated by a single-mode cavity. Tripartite nonlocality is observed in the atom-light-mirror system, as demonstrated by the violation of the Mermin-Klyshko (MK) inequality. It has been shown [C. Genes, et al., PRA 77, 050307 (R) (2008)] that tripartite entanglement is optimized when the cavity is resonant with the anti-Stokes sideband of the driving laser and the atomic frequency matches the Stokes one. However, we show that this is not the case for the nonlocality. The MK function achieves minima when the atoms are resonant with both the Stokes and anti-Stokes sidebands, and unexpectedly, we find violation of the MK inequality only in a parameter region where entanglement is far from being maximum. A negative relation exists between nonlocality and entanglement with consideration of the possibility of bipartite nonlocality in the violation of the MK inequality. We also study the non-classicality of the mirror by post-selected measurements, e.g. Geiger-like detection, on the cavity and/or the atoms. We show that with feasible parameters Geiger-like detection on the atoms can effectively induce mechanical non-classicality. PACS numbers:The lack of observation of quantum effects at the macroscopic scale reinforces the conjecture that macroscopic objects are governed by classical physics, while the microscopic world is ruled by quantum mechanics. However, quantum mechanics intrinsically shows no limitation to describe largescale/massive systems [1]. Preparing macroscopic quantum states is of vital importance for understanding fundamental issues in quantum mechanics, such as decoherence and the quantum-to-classical transition [2], collapse models of the wave function [3], and so on. Optomechanics, addressing the coupling of optical and mechanical degrees of freedom via radiation pressure [4], provides an ideal platform to generate and control quantum mesoscopic/macroscopic states of mechanical systems thanks to its intrinsic nonlinear light-matter interactions.Over the past few years, successful advances in nano-and micro-mechanical engineering, in particular mechanical oscillators cooled into (or close to) their ground state [5,6], have made it possible to prepare mechanical quantum states. Preparing quantum states either for the light mode or the mechanical oscillator is a fascinating (though challenging) goal in the field of optomechanics [7,8]. Nonclassical mechanical states can be generated by the optomechanical nonlinearity intrinsic in the strong coupling regime [9,10], by injecting squeezed light into the cavity (the squeezing is thus transferred from light to the mechanical degree of freedom) [11,12], by post-selected measurements on the optical field [13,14], and so on.Recently, it has been reported that hybrid atom-assisted optomechanics shows advantages in many aspects [15]. To name but a few, atoms induce an additional nonlinear effect, which enhances the optomechanical interaction and...

show abstract

Definitions of multipartite nonlocality

Cited by 197 publications

References 28 publications

Theory of Genuine Tripartite Nonlocality of Gaussian States

Theory of Genuine Tripartite Nonlocality of Gaussian States

Genuine multipartite nonlocality of permutationally invariant Gaussian states

More nonlocality with less entanglement in a tripartite atom‐optomechanical system

Contact Info

Product

Resources

About