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

Yes. The states $|{\Phi }^{+}⟩$ and $|{\Phi }^{-}⟩$ are orthogonal, sinceA joint projective measurement in the Bell basis therefore distinguishes them with certainty. Concretely, a controlled-NOT followed by a Hadamard gate converts the Bell basis into the computational basis before measurement.