Bell-state nondemolition measurement ($P_{z,x}=\frac{1}{4}(I+z{Z}_A{Z}_B)(I+x{X}_A{X}_B)$)

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.