Bell-basis measurement

A Bell-basis measurement is the four-outcome projective measurement whose projectors are onto the four Bell states. It jointly measures two qubits and is the sender's measurement in quantum teleportation.

A device implementing a Bell-basis measurement on two qubits. A complete analyzer distinguishes all four Bell states. A basic passive linear optics analyzer for two polarization qubits uses a balanced beam splitter, polarizing beam splitters and single-photon detectors. Its ideal unambiguous success probability is $1/2$: the two opposite-polarization Bell states have distinct click patterns, while the two same-polarization Bell states remain mutually ambiguous. Additional physical resources can change this restriction. A destructive analyzer absorbs the measured photons; it need not preserve the detected Bell state.

The Bell states are joint eigenstates of commuting $Z_A{Z}_B$ and $X_A{X}_B$. Two shared Bell state meter pairs realize their two entanglement-assisted nondemolition parity measurements using spacelike local circuits. Their projector products give the four rank-one Bell state outcomes and preserve each input Bell state. The globally identified outcome requires later local operations and classical communication.