= Entanglement-assisted discrimination of a Pauli basis
{title2=$(U_j\otimes I)|\phi_+\rangle$}
The four <unitary operators> $I,Z,X,iY$ can be identified with one use when an input <qubit> is entangled with a reference <ancilla qubit>. Applying the unknown operation to one half of $|\phi_+\rangle$ produces the four <orthogonal> <Bell states>, which a <Bell-basis measurement> distinguishes exactly. For operators $VU_jV^\dagger$ in any known <orthonormal basis>, prepare $(V\otimes I)|\phi_+\rangle$ and apply $V^\dagger$ after the unknown call. This reduces to the same <quantum channel discrimination> protocol. Direct expansion proves the four output identities; equivalently, their overlaps are $\operatorname{Tr}(U_j^\dagger U_k)/2=\delta_{jk}$.
Back to article page
