  We consider the Minkowskian norm of the n-photon Stokes tensor, a scalar
invariant under the group realized by the transformations of stochastic local
quantum operations and classical communications (SLOCC). This invariant is
offered as a candidate entanglement measure for n-qubit states and discussed in
relation to measures of quantum state entanglement for certain important
classes of two-qubit and three-qubit systems. This invariant can be directly
estimated via a quantum network, obviating the need to perform laborious
quantum state tomography. We also show that this invariant directly captures
the extent of entanglement purification due to SLOCC filters.
