Dimension-Free Entanglement Detection in Multipartite Werner States

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