Positive maps from the Walled Brauer Algebra

Abstract

Starting from the Walled Brauer Algebra, we present matrix inequalities in the Löwner order for variables from the positive cone. These inequalities contain partial transpose and reshuffling operations, and can be understood as positive multilinear maps. In turn, we show that these positive multilinear maps are in one-to-one correspondence with entanglement witnesses showing U ⊗(n−k) ⊗ Ū ⊗k -invariance.

Werner states from diagrams

“…Significant results on the properties of Werner states include detailed understanding of structure and entanglement properties for bipartite and tripartite systems of arbitrary local dimension [2,11] and general results on entanglement witnesses [12,13]. In this paper, we extend our own previous work on pure and mixed Werner states of arbitrarily many qubits.…”