  In this short note, we show that any non-constant quantity defined on density
matrices that is additive on tensor products and invariant under permutations
cannot be "more than asymptotically continuous." The proof can be adapted to
show that any additive entanglement measure (on any number of parties) that is
invariant under local unitary operations also cannot be more than
asymptotically continuous. The proof is a direct consequence of generalizing a
protocol in arXiv:0804.4118 for embezzling entanglement.
