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Quantum Physics

arXiv:2108.08720 (quant-ph)
[Submitted on 19 Aug 2021 (v1), last revised 11 Oct 2022 (this version, v3)]

Title:Dimension-free entanglement detection in multipartite Werner states

Authors:Felix Huber, Igor Klep, Victor Magron, Jurij Volčič
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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.
Comments: updated abstract
Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Optimization and Control (math.OC)
MSC classes: 81P42, 46N50, 20C35, 90C22, 81-08, 16R30, 13J30
Cite as: arXiv:2108.08720 [quant-ph]
  (or arXiv:2108.08720v3 [quant-ph] for this version)
  https://doi.org/10.48550/arXiv.2108.08720
Journal reference: Communications in Mathematical Physics 396, 1051-1070 (2022)
Related DOI: https://doi.org/10.1007/s00220-022-04485-9

Submission history

From: Felix Huber [view email]
[v1] Thu, 19 Aug 2021 14:41:09 UTC (23 KB)
[v2] Sun, 5 Sep 2021 18:39:31 UTC (23 KB)
[v3] Tue, 11 Oct 2022 13:32:28 UTC (23 KB)
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