  In this paper, we establish explicit relationship between decomposition
numbers of quantized walled Brauer algebras and those for either Hecke algebras
associated to certain symmetric groups or (rational) $q$-Schur algebras over a
field $\kappa$. This enables us to use Ariki's result \cite{Ar} and
Varagnolo-Vasserot's result \cite{VV} to compute such decomposition numbers via
inverse Kazhdan-Lusztig polynomials associated with affine Weyl groups of type
$A$ if the ground field is $\mathbb C$.
