Inequality between Holevo capacity and coherent information of quantum channels

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 $chi(mathcal{N})$.