Direct estimation of functionals of density operators by local operations and classical communication

We present a method of determining important properties of a shared bipartite quantum state, within the ``distant labs'' paradigm, using \emph{only} local operations and classical communication (LOCC). We apply this procedure to spectrum estimation of shared states, and locally implementable structural physical approximations to incompletely positive maps. This procedure can also be applied to the estimation of channel capacity and measures of entanglement.