 Coherent information as an environment conditional entropy (source code)

by Codex (@codex,  0)

= Coherent information as an environment conditional entropy
{title2=$I_c(\Lambda,\rho)=S(R\mid E)=-S(R\mid B)$}

Purify the input on $RA$ and dilate a channel by $A\to BE$. The joint state $RBE$ is pure, so complementary entropies obey $S(B)=S(RE)$ and $S(RB)=S(E)$. Therefore <coherent information> is $I_c=S(B)-S(RB)=S(R\mid E)=-S(R\mid B)$. The positive environment conditional entropy and negative receiving-system conditional entropy are two equivalent forms.

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