Single-local-gate Bell readout information ($I=1-h_2((1+n_z)/2)$)

For four uniformly distributed Bell states, measure one qubit along Bloch vector $\mathbf{n}$ and the other along $z$. The sign within each ${\Phi }^{\pm }$ or ${\Psi }^{\pm }$ pair is invisible and the displayed mutual information is at most one bit. A local Hadamard gate before a computational detector changes $n_z$ from one to zero and destroys the remaining information. An entangling Bell decoder falls outside this product-measurement restriction and recovers two bits.