Dimension-free entanglement detection in multipartite Werner states [article]

Felix Huber, Igor Klep, Victor Magron, Jurij Volčič
2021 arXiv   pre-print
Werner states are multipartite quantum states that are invariant under the diagonal conjugate action of the unitary group. This paper gives a characterization of their entanglement that is independent of the underlying local Hilbert space. For a given Werner state, the construction of a dimension-free entanglement 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
more » ... o positive polynomials in the entries of a Gram matrix, and the second one is based on a sum-of-squares certificate for the positivity of trace polynomials in noncommuting variables.
arXiv:2108.08720v2 fatcat:4ssl52fndfb35omxudgxgzejda