 Local indistinguishability of Bell-state phase

The Bell states $|{\Phi }^{+}⟩=(|00⟩+|11⟩)/\sqrt{2}$ and $|{\Phi }^{-}⟩=(|00⟩-|11⟩)/\sqrt{2}$ both have reduced state $I/2$ on either qubit. No measurement on one qubit alone can distinguish their relative sign.