= Entanglement-assisted capacity of a qubit depolarizing channel
{title2=$C_E=2-H_4(1-p,p/3,p/3,p/3)$}
For the <quantum depolarizing channel> applying the identity with probability $1-p$ and each nonidentity <Pauli operator> with probability $p/3$, the entanglement-assisted classical capacity is the displayed number of <bits> per use. Here $H_4$ is <Shannon entropy> of the four listed probabilities. Its unassisted product-state capacity is $1-h_2(2p/3)$. Both vanish at $p=3/4$. If $q$ instead denotes replacement by $I/2$, then $p=3q/4$ and complete depolarization is at $q=1$. https://arxiv.org/abs/quant-ph/9904023[The original entanglement-assisted capacity paper] gives the depolarizing-channel formula.
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