Dimension-Free Entanglement Detection in Multipartite Werner States
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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
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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