  We develop separability criteria to identify non-$k$-separability $(k =
2,3,\ldots,n)$ and genuine multipartite entanglement in different classes of
mixed $n$-partite quantum states using elements of density matrices. With the
help of these criteria, we detect non-$k$-separability in $n$-qudit GHZ and W
states respectively added with white noise. We also discuss the experimental
implementation of our criteria by means of local observables.
