 Two-component Bell resource in dense coding

With phase/parity labels $(u,v)$ encoded by $X^v{Z}^u$, a resource $a|{\Phi }^{+}⟩+b|{\Phi }^{-}⟩$ gives intended-label probability $|a{|}^2$ and phase-label-flip probability $|b{|}^2$ under a Bell-basis measurement. This follows because the local Pauli operator maps the two orthogonal components into the two Bell states whose phase label differs. The resource is a coherent pure state, even though its measured label statistics form a classical noisy channel.