Dimension-Free Entanglement Detection in Multipartite Werner States

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Standard

Dimension-Free Entanglement Detection in Multipartite Werner States. / Huber, Felix; Klep, Igor; Magron, Victor; Volčič, Jurij.

I: Communications in Mathematical Physics, Bind 396, 2022, s. 1051–107.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Huber, F, Klep, I, Magron, V & Volčič, J 2022, 'Dimension-Free Entanglement Detection in Multipartite Werner States', Communications in Mathematical Physics, bind 396, s. 1051–107. https://doi.org/10.1007/s00220-022-04485-9

APA

Huber, F., Klep, I., Magron, V., & Volčič, J. (2022). Dimension-Free Entanglement Detection in Multipartite Werner States. Communications in Mathematical Physics, 396, 1051–107. https://doi.org/10.1007/s00220-022-04485-9

Vancouver

Huber F, Klep I, Magron V, Volčič J. Dimension-Free Entanglement Detection in Multipartite Werner States. Communications in Mathematical Physics. 2022;396:1051–107. https://doi.org/10.1007/s00220-022-04485-9

Author

Huber, Felix ; Klep, Igor ; Magron, Victor ; Volčič, Jurij. / Dimension-Free Entanglement Detection in Multipartite Werner States. I: Communications in Mathematical Physics. 2022 ; Bind 396. s. 1051–107.

Bibtex

@article{34c93f6c8e2c45e0bde19676bcf473fa,
title = "Dimension-Free Entanglement Detection in Multipartite Werner States",
abstract = "Werner states are multipartite quantum states that are invariant under the diagonal conjugate action of the unitary group. This paper gives a complete characterization of their entanglement that is independent of the underlying local Hilbert space: for every entangled Werner state there exists a dimension-free entanglement witness. The construction of such a witness is formulated as an optimization problem. To solve it, two semidefinite programming hierarchies are introduced. The first one is derived using real algebraic geometry applied to positive polynomials in the entries of a Gram matrix, and is complete in the sense that for every entangled Werner state it converges to a witness. The second one is based on a sum-of-squares certificate for the positivity of trace polynomials in noncommuting variables, and is a relaxation that involves smaller semidefinite constraints.",
author = "Felix Huber and Igor Klep and Victor Magron and Jurij Vol{\v c}i{\v c}",
note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2022",
doi = "10.1007/s00220-022-04485-9",
language = "English",
volume = "396",
pages = "1051–107",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer",

}

RIS

TY - JOUR

T1 - Dimension-Free Entanglement Detection in Multipartite Werner States

AU - Huber, Felix

AU - Klep, Igor

AU - Magron, Victor

AU - Volčič, Jurij

N1 - Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2022

Y1 - 2022

N2 - Werner states are multipartite quantum states that are invariant under the diagonal conjugate action of the unitary group. This paper gives a complete characterization of their entanglement that is independent of the underlying local Hilbert space: for every entangled Werner state there exists a dimension-free entanglement witness. The construction of such a witness is formulated as an optimization problem. To solve it, two semidefinite programming hierarchies are introduced. The first one is derived using real algebraic geometry applied to positive polynomials in the entries of a Gram matrix, and is complete in the sense that for every entangled Werner state it converges to a witness. The second one is based on a sum-of-squares certificate for the positivity of trace polynomials in noncommuting variables, and is a relaxation that involves smaller semidefinite constraints.

AB - Werner states are multipartite quantum states that are invariant under the diagonal conjugate action of the unitary group. This paper gives a complete characterization of their entanglement that is independent of the underlying local Hilbert space: for every entangled Werner state there exists a dimension-free entanglement witness. The construction of such a witness is formulated as an optimization problem. To solve it, two semidefinite programming hierarchies are introduced. The first one is derived using real algebraic geometry applied to positive polynomials in the entries of a Gram matrix, and is complete in the sense that for every entangled Werner state it converges to a witness. The second one is based on a sum-of-squares certificate for the positivity of trace polynomials in noncommuting variables, and is a relaxation that involves smaller semidefinite constraints.

UR - http://www.scopus.com/inward/record.url?scp=85137020286&partnerID=8YFLogxK

U2 - 10.1007/s00220-022-04485-9

DO - 10.1007/s00220-022-04485-9

M3 - Journal article

AN - SCOPUS:85137020286

VL - 396

SP - 1051

EP - 1107

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

ER -

ID: 319245780