= Solution
Bob must discard both results. An unread X <quantum measurement>[measurement] gives $\rho_X=p_+|+\rangle\langle+|+p_-|-\rangle\langle-|$. Each of these two X <eigenstates> gives Z outcomes with <probabilities> $1/2,1/2$. The final unread Z <quantum measurement>[measurement] therefore gives
$$
\boxed{\rho_{B,\rm final}=\frac12|0\rangle\langle0|+\frac12|1\rangle\langle1|=I/2.}
$$
Equivalently, in the <Bloch vector>[Bloch-vector] description the first <quantum measurement>[measurement] retains only the X component, and the second retains only the Z component, leaving none. The final state is independent of the original $\alpha,\beta$.
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