  After introducing the partially separable concept, we proved the equivalence
between the partial separability of a given $m$-partite subsystem with $m$
qubits and the purity of states of this $m$-partite subsystem for a pure state
in multipartite systems with arbitrary finite $n(>m)$ qubits. Furthermore, we
give out the operational realizations (corollaries) of our theorem, which are
the sufficient and necessary criterions of partial separability of states and
can be used to classification of states. Our results are helpful to understand
and describe quantum entanglement in multipartite systems.
