Numerical analysis of entanglement properties of density matrices in C²⊗C² systems

Quantum entanglement is an enigmatic and powerful property that has attracted much attention due to its usefulness in new ways of communications, like quantum teleportation and quantum key distribution. Much effort has been done to quantify entanglement. Indeed, there exist some well-established separability criterion and analytical formulas for the entanglement of bipartite systems. In both, the crucial element is the partial transpose of the density matrix. In this paper, we show numerically that one can also have information about the entanglement of bipartite state, in C²⊗C², without looking at the partial transpose. We furthermore study properties of disentanglement operation, as well as properties of the relative entropy.