  Using a change of basis in the algebra of symmetric functions, we compute the
moments of the Hermitian Jacobi process. After a careful arrangement of the
terms and the evaluation of the determinant of an `almost upper-triangular'
matrix, we end up with a moment formula which is considerably simpler than the
one derived in \cite{Del-Dem}. As an application, we propose the Hermitian
Jacobi process as a dynamical model for optical fibers MIMO channels and
compute its Shannon capacity for small enough power at the transmitter.
Moreover, when the size of the Hermitian Jacobi process is larger than the
moment order, our moment formula may be written as a linear combination of
balanced terminating ${}_4F_3$-series evaluated at unit argument.
