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The final printed direction is reversed under the majorization convention stated in the same part. A completely depolarizing unital quantum channel sends a pure qubit state to $I/2$, giving spectra $r=(1,0)$ and $s=(1/2,1/2)$. The proposed $r\prec s$ fails already at the first partial sum, since $1>1/2$. The valid conclusion isHere is its general proof. Choose eigenbases $\rho ={\sum }_i{r}_i|u_i⟩⟨u_i|$ and $\sigma ={\sum }_j{s}_j|v_j⟩⟨v_j|$, and define the eigenvalue mixing matrix of a unital quantum channelIts entries are nonnegative by positivity. Trace preservation gives ${\sum }_j{A}_{ji}=1$ for every column. Unitality gives ${\sum }_i{A}_{ji}=⟨v_j|\Lambda (I)|v_j⟩=1$ for every row. Thus $A$ is a doubly stochastic matrix, and linearity givesThe supplied doubly stochastic characterization of majorization then yields $s\prec r$, completing the intended corrected result. This proves spectral majorization under a unital quantum channel. A unital quantum channel can make a spectrum more uniform; it cannot generally make the output spectrum majorize the input. The counterexample resolves the false printed assertion rather than treating the reversed inequality as a convention change.