  A Bayesian functorial characterization of the classical relative entropy (KL
divergence) of finite probabilities was recently obtained by Baez and Fritz.
This was then generalized to standard Borel spaces by Gagn\'e and Panangaden.
Here, we provide preliminary calculations suggesting that the
finite-dimensional quantum (Umegaki) relative entropy might be characterized in
a similar way. Namely, we explicitly prove that it defines an affine functor in
the special case where the relative entropy is finite. A recent non-commutative
disintegration theorem provides a key ingredient in this proof.
