  The detection of multipartite entanglement in arbitrary dimensional systems
is investigated. We derive useful $k$-separability criteria of mixed
$n$-partite ($n\geq 3$) quantum states to detect $k$-nonseparable $n$-partite
quantum states. Our criteria can be expressed by the elements of the density
matrix, which allows a simple and practical evaluation and computation. They
are experimentally accessible without quantum state tomography.
