I am referring to the following definition: "Given a channel $\Phi$ on $\mathcal{H}$ and a subspace $\mathcal{C}$, we say $\mathcal{C}$ is private for $\Phi$ if there is a density operator $\rho_0$ such that $\Phi(\rho) = \rho_0$ for all $\rho$ supported on $\mathcal{C}$; that is, for all $\rho$ on $\mathcal{H}$ with $\rho = P_{\mathcal{C}} \rho P_{\mathcal{C}}$ and where $P_{\mathcal{C}}$ is the projection onto $\mathcal{C}$."
So what I think is happening is that everything is getting mapped to the same point (?), does that mean it is being decodded? Am I on the right track?