Quasi multipartite entanglement measure based on quadratic functions

Abstract

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.