Optimizing entanglement in two-qubit systems

We investigate entanglement in two-qubit systems using a geometric representation based on the minimum of essential parameters. The states are X-shaped and host pairs of identical populations while reducing the number of coherences involved. A geometric L-measure of entanglement is introduced as the distance between the points that represent entangled states and the closest point that defines separable states. Our results give a geometric meaning to the Hill-Wootters concurrence C since L coincides with C. Furthermore, unlike C, the measure L distinguishes the rank of states with maximum entanglement. We construct a time-dependent two-qubit state, traced out over the complementary components of a pure tetra-partite system, and find that its one-qubit states share the same entropy. The entanglement measure results bounded from above by the envelope of the minima of such entropy.