Let $\mathcal{N} : M_n \to M_n$ be a unital quantum channel (hence trace preserving and completely positive).
Do we have the inequality $Q^{(1)}(\mathcal{N}) \leq \chi(\mathcal{N})$ ?
Here $\chi(\mathcal{N})$ is the Holevo capacity (or Holevo information) of $T$ and $Q^{(1)}(\mathcal{N})$ is the coherent information of $\mathcal{N}$.
I ask this question since I know that $Q(\mathcal{N}) \leq C(\mathcal{N})$ where $Q(\mathcal{N})$ and $C(\mathcal{N})$ are the regularized version of $Q^{(1)}(\mathcal{N})$ and $\chi(\mathcal{N})$.