Data-processing inequality for coherent information
= Data-processing inequality for coherent information
{title2=$I(A\rangle B)-I(A\rangle B\prime)=I(A:E|B\prime)\geq0$}
A <quantum channel> on the receiving system cannot increase <coherent information>: $I(A\rangle B)_\rho\geq I(A\rangle B^{\prime})_\sigma$. Dilate the channel to a <linear isometry of Hilbert spaces> $B\to B^{\prime}E$. The difference is $I(A:E|B^{\prime})$ of the dilated state, nonnegative by <Strong subadditivity of Von Neumann entropy>.