Verifying genuine multipartite entanglement of the whole from its separable parts

Mičuda, Michal; Stárek, Robert; Provazník, Jan; Leskovjanová, Olga; Mišta, Ladislav

doi:10.1364/optica.6.000896

Cited by 8 publications

(19 citation statements)

References 31 publications

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“…The matrix A (3,2) must be constructed in such a way that there are no product, across the cuts B|AC and C|AB, nonzero vectors perpendicular to the subspace spanned by vectors (11). Let us concentrate on the first case, while for the second one the reasoning goes along the same lines with the only difference that the matrix elements are reshuffled in a certain manner.…”

Section: General Casementioning

confidence: 99%

“…The proof is moved to Appendix C. These forms can be further restricted by considering non-existence of other vectors in a subspace, e.g., |+ |i | j and |− |i | j , i, j = 0, 1. One can also reduce the number of parameters at the very beginning and consider only matrices of the form: 11 , with a, b ≥ 0 and two-by-two matrices A i j . This is due to the fact that we can always write A = i, j |i j| ⊗ A i j and perform 1 ⊗ U (•)1 ⊗ V † with U , V stemming from the singular value decomposition of A 00 (this also applies to other blocks).…”

Section: General Casementioning

confidence: 99%

“…Genuinely entangled states are a crucial resource for many quantum information processing protocols in networks (see, e.g., [1][2][3][4][5]). Their exhaustive characterization is thus of vital importance for the success of future quantum technologies, and for this reason, it has been the subject of intensive, both theoretical (see, e.g., [6][7][8][9]) and experimental (see, e.g., [10][11][12]), studies.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An approach to constructing genuinely entangled subspaces of maximal dimension

Demianowicz¹,

Augusiak²

2020

Quantum Inf Process

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Genuinely entangled subspaces (GESs) are the class of completely entangled subspaces that contain only genuinely multiparty entangled states. They constitute a particularly useful notion in the theory of entanglement but also have found an application, for instance, in quantum error correction and cryptography. In a recent study (Demianowicz and Augusiak in Phys Rev A 98:012313, 2018), we have shown how GESs can be efficiently constructed in any multiparty scenario from the so-called unextendible product bases. The provided subspaces, however, are not of maximal allowable dimensions, and our aim here is to put forward an approach to building such. The method is illustrated with few examples in small systems. Connections with other mathematical problems, such as spaces of matrices of equal rank and the numerical range, are discussed. Keywords Genuinely entangled subspace • Genuinely multiparty entangled • Completely entangled subspace • Entanglement • Spaces of matrices of bounded rank Maciej Demianowicz

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Section: General Casementioning

confidence: 99%

Section: General Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An approach to constructing genuinely entangled subspaces of maximal dimension

Demianowicz¹,

Augusiak²

2020

Quantum Inf Process

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“…So far, only examples of qubit states carrying genuine multipartite entanglement which can be verified solely from separable two-qubit reduced states (marginals) were found [7,8] and demonstrated experimentally [15]. In all these cases, the set of marginals used to certify the entanglement comprised all two-qubit marginals.…”

Section: Introductionmentioning

confidence: 99%

“…States with genuine multipartite entanglement which can be confirmed using only the elements of the minimal set where found for all configurations of up to six qubits using the iterative numerical search algorithm [9] combining the machinery of entanglement witnesses [17,18] with the tools of semidefinite programming [19]. The best example obtained was three-qubit [8] with the lowest witness mean being roughly three times smaller than the witness mean for the scenario in which all two-qubit marginals are known [8,15]. Moreover, the difference is even more pronounced compared to other theoretically predicted witness means [20] of already successfully implemented multipartite entanglement witnesses experiments [21].…”

Section: Introductionmentioning

confidence: 99%

Convicting emergent multipartite entanglement with evidence from a partially blind witness

Nordgren¹,

Leskovjanová²,

Provazník³

et al. 2021

Preprint

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Genuine multipartite entanglement underlies correlation experiments corroborating quantum mechanics and it is an expedient empowering many quantum technologies. One of many counterintuitive facets of genuine multipartite entanglement is its ability to exhibit an emergent character, that is, one can infer its presence in some multipartite states merely from a set of its separable marginals. Here, we show that the effect can be found also in the context of Gaussian states of bosonic systems. Specifically, we construct examples of multimode Gaussian states carrying genuine multipartite entanglement which can be verified solely from separable nearest-neighbour two-mode marginals. The key tool of our construction is a genuine multipartite entanglement witness acting only on some two-mode reductions of the global covariance matrix, which we find by a numerical solution of a semi-definite programme. We also propose an experimental scheme for preparation of the simplest three-mode state, which requires interference of three correlatively displaced squeezed beams on two beam splitters. Besides revealing the concept of emergent genuine multipartite entanglement in the Gaussian scenario and bringing it closer to experimentally testable form, our results pave the way to effective diagnostics methods of global properties of multipartite states without complete tomography.

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Certifying emergent genuine multipartite entanglement with a partially blind witness

et al. 2022

Self Cite

View full text Add to dashboard Cite

Genuine multipartite entanglement underlies correlation experiments corroborating quantum mechanics and it is an expedient empowering many quantum technologies. One of many counterintuitive facets of genuine multipartite entanglement is its ability to exhibit an emergent character. That is, one can infer its presence in some multipartite states merely from a set of its separable marginals. Here we show that the effect can also be found in the context of Gaussian states of bosonic systems. Specifically, we construct examples of multimode Gaussian states carrying genuine multipartite entanglement which can be verified solely from separable nearestneighbor two-mode marginals. The key tool of our construction is an entanglement witness acting only on some two-mode reductions of the global covariance matrix, which we find by a numerical solution of a semidefinite program. We also propose an experimental scheme for preparation of the simplest three-mode state, which requires interference of three correlatively displaced squeezed beams on two beam splitters. Besides revealing the concept of emergent genuine multipartite entanglement in the Gaussian scenario and bringing it closer to experimentally testable form, our results pave the way to effective diagnostics methods of global properties of multipartite states without complete tomography.

show abstract

Verifying genuine multipartite entanglement of the whole from its separable parts

Cited by 8 publications

References 31 publications

An approach to constructing genuinely entangled subspaces of maximal dimension

An approach to constructing genuinely entangled subspaces of maximal dimension

Convicting emergent multipartite entanglement with evidence from a partially blind witness

Certifying emergent genuine multipartite entanglement with a partially blind witness

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