= High-noise capacity ratio for qubit depolarization
{title2=$\lim C_E/C_{\mathrm{prod}}=3$}
With <Bloch vector> retention $\eta\to0$, the unassisted product-state capacity of a <quantum depolarizing channel> is $\eta^2/(2\ln2)+O(\eta^4)$. Its entanglement-assisted capacity is $3\eta^2/(2\ln2)+O(\eta^3)$, obtained by expanding <Shannon entropy> around the uniform four-outcome distribution. Consequently their limiting ratio is three, independent of the linear noise-parameter convention.
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