  We develop a new entanglement measure by extending Jaeger's Minkowskian norm
entanglement measure. This measure can be applied to a much wider class of
multipartite mixed states, although still "quasi" in the sense that it is still
incapable of dividing precisely the sets of all separable and entangled states.
As a quadratic scalar function of the system density matrix, the quasi measure
can be easily expressed in terms of the so-called coherence vector of the
system density matrix, by which we show the basic properties of the quasi
measure including (1) zero-entanglement for all separable states, (2)
invariance under local unitary operations, and (3) non-increasing under local
POVM (positive operator-valued measure) measurements. These results open up
perspectives in further studies of dynamical problems in open systems,
especially the dynamic evolution of entanglement, and the entanglement
preservation against the environment-induced decoherence effects.
