  The pure states that can be uniquely determined among all (UDA) states by
their marginals are essential to efficient quantum state tomography. We
generalize the UDA states from the context of pure states to that of arbitrary
(no matter pure or mixed) states, motivated by the efficient state tomography
of low-rank states. We call the \emph{additivity} of $k$-UDA states for three
different composite ways of tensor product, if the composite state of two
$k$-UDA states is still uniquely determined by the $k$-partite marginals for
the corresponding type of tensor product. We show that the additivity holds if
one of the two initial states is pure, and present the conditions under which
the additivity holds for two mixed UDA states. One of the three composite ways
of tensor product is also adopted to construct genuinely multipartite entangled
(GME) states. Therefore, it is effective to construct multipartite $k$-UDA
state with genuine entanglement by uniting the additivity of $k$-UDA states and
the construction of GME states.
