For a quantum channel $\Lambda$, the corresponding bipartite state is $\rho=(I\otimes\Lambda)(|\Phi\rangle\langle\Phi|)$, where $|\Phi\rangle=\frac{1}{\sqrt{n}}\sum_{i}|ii\rangle$.

The maximal singlet fraction is defined as $f(\rho)=Max_{\psi}\langle\psi|\rho|\psi\rangle$. where $\psi$ is maximal entangled state.

If the second system passes another quantum channel,


Is it true that $f(\rho)\geq f(\rho')$? How to prove it?


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