‎Let $C$ and $D$ be positive operators such that $C\leq D$ and $D$ be invertible‎. ‎We show that there exists a trace preserving unital completely positive map $\Phi_{C,D}:\mathbb{B}(\mathcal{H})\rightarrow \mathbb{B}(\mathcal{H})$ such that ‎the ‎block ‎operator ‎matrices ‎\begin{equation*}‎ ‎\left(‎ ‎\begin{array}{cc}‎ ‎\Phi_{C,D}(A) & C \\‎ ‎C & \Phi_{C,D}(B) \\‎ ‎\end{array}‎ ‎\right)‎ ‎\end{equation*}‎ are positive‎, ‎for all positive operators $A$ and $B$ such that $D=A\sharp B$‎.

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