  Many-body quantum systems can be characterised using the notions of
\emph{k}-separability and entanglement depth. A quantum state is
\emph{k}-separable if it can be expressed as a mixture of \emph{k} entangled
subsystems, and its entanglement depth is given by the size of the largest
entangled subsystem. In this paper we propose a multipartite entanglement
measure that satisfies the following criteria: (i) it can be used with both
pure and mixed states; (ii) it is encoded in a single element of the density
matrix, so it does not require knowledge of the full spectrum of the density
matrix; (iii) it can be applied to large systems; and (iv) it can be
experimentally verified. The proposed method allows the certification of
\emph{non-k}-separability of a given quantum state. We show that the proposed
method successfully classifies three-qubit systems into known stochastic local
operations and classical communication (SLOCC) classes, namely bipartite,
\mbox{W-,} and GHZ-type entanglement. Furthermore, we characterise the
\emph{non-k}-separability in known nine SLOCC classes of four-qubit states,
absolutely maximally entangled states for five and six qubits and for arbitrary
size qubit Dicke states.
