Regensburg 2022 – scientific programme

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QI: Fachverband Quanteninformation

QI 9: Quantum Correlations

QI 9.1: Talk

Thursday, September 8, 2022, 09:30–09:45, H8

Dimension-free entanglement detection in multipartite Werner states — •Felix Huber¹, Igor Klep², Victor Magron³, and Jurij Volčič⁴ — ¹Institute of Theoretical Physics, Jagiellonian University, 30-348 Kraków, Poland — ²Faculty of Mathematics and Physics, University of Ljubljana, Slovenia — ³LAAS-CNRS & Institute of Mathematics from Toulouse, France — ⁴Department of Mathematical Sciences, University of Copenhagen, Denmark

Werner states are multipartite quantum states that are invariant under the diagonal conjugate action of the unitary group. We give 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 an entanglement 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.