 Bell-state measurement

A Bell-state measurement distinguishes the four two-qubit Bell states. Ideally its four measurement operators are the rank-one orthogonal projectors onto $|{\Phi }^{+}⟩$, $|{\Phi }^{-}⟩$, $|{\Psi }^{+}⟩$ and $|{\Psi }^{-}⟩$. It measures joint parity and relative-phase information, rather than the two qubits separately in one local basis.

A circuit realization applies a CNOT gate with the first qubit as control, then a Hadamard gate to that qubit, followed by computational-basis measurements of both. These gates map the Bell basis to four distinct computational-basis states. A complete result therefore carries two classical bits and supplies the correction label in ideal quantum teleportation. A restricted experimental analyzer may distinguish fewer than all four outcomes.