Measurement direction of a CNOT interaction ($U=I_S\otimes Q_{+}+Z_S\otimes Q_{-}$)

A CNOT gate can correlate either the original control's computational label with a computational pointer, or the original target's sign-basis label with a sign-basis pointer. For the second interpretation prepare the original control in $|+⟩$ and read it in the Hadamard basis. Its two pointer states become $|+⟩$ and $|-⟩$, measuring $X$ on the original target. An apparatus role therefore depends on the ready state and readout as well as the measurement interaction.