**Input:** Two entangled qubits in Bell state $|\Phi^{+}\rangle = \frac{1}{\sqrt{2}} \big(|00\rangle + |11\rangle\big)$.

**Goal:**  Change the two-qubit state, without adding a global phase, to $|\Psi^{-}\rangle = \frac{1}{\sqrt{2}} \big(|01\rangle - |10\rangle\big)$.