  The definition of quantum discord is generalized to allow for any concave
entropy function, and its non-negativity strengthens the subadditivity
condition for that entropy function. In a sense, this condition is intermediate
in strength between subadditivity and strong subadditivity, hence called firm
subadditivity, allowing one to further classify entropy functions based on
whether they satisfy this intermediate condition. It is proven that the
quadratic entropy $1-\Tr(\rho^2)$ satisfies the firm subadditivity condition,
whereas some other subadditive Tsallis entropies are not firmly subadditive.
