Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 2 / 10D / b / iii / Solution

Yes. Alice and Bob both measure in the Hadamard basis $|+⟩,|-⟩$. The identitiesshow that their outcomes agree for $|{\Phi }^{+}⟩$ and differ for $|{\Phi }^{-}⟩$. After exchanging one classical bit they know which state they had. This is the LOCC discrimination of two Bell states.