Reexamination of determinant-based separability test for two qubits

It was shown in Augusiak et al. [Phys. Rev. A 77, 030301(R) (2008)] that discrimination between entanglement and separability in a two-qubit state can be achieved by a measurement of a single observable on four copies of it. Moreover, a pseudoentanglement monotone π was proposed to quantify entanglement in such states. The main goal of this Brief Report is to show that the close relationship between π and concurrence reported there is a result of sharing the same underlying construction of a spin-flipped matrix. We also show that monogamy of entanglement can be rephrased in terms of π and prove the factorization law for π.