One primary goal of entanglement theory is to determine which conversions of quantum states are possible using LOCC. Entanglement of bipartite pure states is well understood, but there are still many questions that can be answered when it comes to mixed states. Finding convertibility conditions for arbitrary mixed entangled states is a daunting task. We investigate entanglement of states that are symmetric under certain group actions, such as Werner states and isotropic states. For example, convex roofs of entanglement monotones can be evaluated for such symmetric states by utilizing the symmetry and the group action. Furthermore, we present necessary and sufficient conditions for determining when pure states can be converted into symmetric states by LOCC.

Coauthor: Gilad Gour