Entanglement Polytopes: Multiparticle Entanglement from Single-Particle Information

Walter, Michael; Doran, Brent; Gross, David J.; Christandl, Matthias

doi:10.1126/science.1232957

Cited by 167 publications

(224 citation statements)

References 81 publications

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“…In [13] a characterization of multipartite entanglement in terms of even just single-party reduced states (actually, singleparty spectra) was given, but under the assumption of dealing with a pure or quasi-pure global state. In [14][15][16] the possibility of dealing with global mixed states is taken into account, and examples are given where twoqubit separable states are only compatible with global entanglement, intended in the sense of lack of total separability (see Section II for definitions).…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

Role of correlations in the two-body-marginal problem

et al. 2014

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“…For more than three qubits there is an infinite number of SLOCC classes and the introduction of families of entanglement classes [5] has been instrumental to shed light into the increasing level of complexity [6]. Recently the concept of entanglement polytopes has provided an insightful geometrical information to discriminate the SLOCC classes [7]. Ratios of polynomial invariants can also be a very useful tool in this context [8].…”

Section: Introductionmentioning

confidence: 99%

Operational entanglement families of symmetric mixedN-qubit states

Bastin

Mathonet²,

Solano³

2015

Phys. Rev. A

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We introduce an operational entanglement classification of symmetric mixed states for an arbitrary number of qubits based on stochastic local operations assisted with classical communication (SLOCC operations). We define families of SLOCC entanglement classes successively embedded into each other, we prove that they are of non-zero measure, and we construct witness operators to distinguish them. Moreover, we discuss how arbitrary symmetric mixed states can be realized in the lab via a one-to-one correspondence between well-defined sets of controllable parameters and the corresponding entanglement families.

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“…In case of pure, multiparticle quantum states, the authors have shown that the features of the global entanglement can be extracted from its local information alone. Unlike the present paper, the approach in [37] is not device-independent. However, extending this idea in device-independent framework may be an interesting research direction.…”

Section: Lemma 1 (Wolf Et Al [30]): Any Two Dichotomic Quantum Measmentioning

confidence: 82%

“…In comparison to this our semi-device independent scenario assumes dimension of only one of the subsystems. Another recent work [37] by Walter et al is also quite worthy to mention here. They have introduced a geometrical object, called entanglement polytope which characterizes the eigenvalues of the single-particle states in any given class of entanglement.…”

Section: Lemma 1 (Wolf Et Al [30]): Any Two Dichotomic Quantum Measmentioning

confidence: 99%

Improvement in device-independent witnessing of genuine tripartite entanglement by local marginals

et al. 2017

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We consider the problem of determining the presence of genuine multipartite entanglement through the violation of Mermin's Bell-type inequality (MI). Though the violation of MI cannot certify the presence of genuine nonlocality, but can certify genuine tripartite entanglement whenever the violation is strictly greater than 2 √ 2. Here we show that MI suffices as genuine entanglement witness even when its value is 2 √ 2 if at least two of the local marginal distributions are not completely random provided the local Hilbert space dimension of at least one of the sub-systems is two. Thus local marginals suffice as semi-device independent genuine entanglement witness. This is intriguing in a sense, as the local properties of a composite system can help to identify its global property. Furthermore, analyzing another quantity constructed from Mermin polynomials we show that genuine entanglement certification task for the correlations with MI violation equal to 2 √ 2 can actually be made fully device independent.PACS numbers: 03.65. Ud, 03.67.Mn Entanglement is considered to be one of the most bizarre nonclassical manifestations of multipartite quantum systems. Linearity of quantum mechanics (QM) allows to build superposed states that cannot be written as product of states of each subsystems and hence resulting in entangled states. Entanglement lies at the core of some of the most puzzling features of QM: the Einstein-Podolski-Rosen (EPR) argument [1], the Schrodinger's steering concept [2], and most importantly the nonlocal behaviour of QM [3]. In the past three decades quantum entanglement has also been established as a useful resource for several information theoretic tasks: quantum cryptography [4], quantum teleportation [5], quantum superdense coding [6] are few noteworthy among many others.While the state of a quantum system composed of only two subsystems can be either separable or entangled, for a quantum system with more than two subsystems the separability properties have a complicated structure. In the multipartite scenario the most dramatic attribute appearing in the picture is the concept of truly or genuinely multipartite entanglement (GME) which cannot be prepared by mixing states that are separable with respect to some partition [7][8][9][10]. Whereas Greenberger, Horne, and Zeilinger established implication of GME in quantum foundations by reveling perfect incompatibility of QM with EPR idea of local deterministic world view [7], significant advantages of it compared to bipartite entanglement has also been established in different practical tasks, namely, extreme spin squeezing [11], high sensitivity in some general metrology tasks [12], quantum computing using cluster states [13], measurement-based quantum computation [14], various quantum communication protocols [15], secret sharing among multiple parties and multiparty quantum network [16]. Despite its importance, characterization and detection of entanglement is quite difficult. Several methods such as tomography of the full state [17], construc...

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Entanglement Polytopes: Multiparticle Entanglement from Single-Particle Information

Cited by 167 publications

References 81 publications

Role of correlations in the two-body-marginal problem

Role of correlations in the two-body-marginal problem

Operational entanglement families of symmetric mixedN-qubit states

Improvement in device-independent witnessing of genuine tripartite entanglement by local marginals

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