Computational-basis intercept-resend attack ($\rho \mapsto {\sum }_{b=0}^1(I\otimes |b⟩⟨b|)\rho (I\otimes |b⟩⟨b|)$)

Measuring the transmitted qubit in the computational basis and forwarding its measured state produces a dephasing channel for users who do not know the outcome. For a Bell state $|{\Psi }^{+}⟩$, the reduced state becomes $(|01⟩⟨01|+|10⟩⟨10|)/2$. It retains perfect $Z$ anticorrelation while destroying $X$ correlation. Thus a single perfectly correlated key basis need not reveal an intercept-resend attack; incompatible-basis correlation tests can.