  The primary goal in the study of entanglement as a resource theory is to find
conditions that determine when one quantum state can or cannot be transformed
into another via local operations and classical communication. This is
typically done through entanglement monotones or conversion witnesses. Such
quantities cannot be computed for arbitrary quantum states in general, but it
is useful to consider classes of symmetric states for which closed-form
expressions can be found. In this paper, we show how to compute the convex roof
of any entanglement monotone for all Werner states. The convex roofs of the
well-known Vidal monotones are computed for all isotropic states, and we show
how this method can generalize to other entanglement measures and other types
of symmetries as well. We also present necessary and sufficient conditions that
determine when a pure bipartite state can be deterministically converted into a
Werner state or an isotropic state.
