A comparative study entanglement, of relative entropy of and negativity

The problem of ordering of two-qubit states imposed by the relative entropy of entanglement (E) in comparison with the concurrence (C) and negativity (N) is studied. Analytical examples of states consistently and inconsistently ordered by the entanglement measures are given. In particular, the states for which any of the three measures imposes order opposite to that given by the other two measures are described. Moreover, examples are given of pairs of the states for which (i) N' = N" and C = C' but E' is different from E", (ii) N' = N" and E' = E" but C differs from C", (iii) E' = E", N' < N" and C > C"; and (iv) states having the same E, C and N but still violating the Bell-Clauser-Horne-Shimony-Holt inequality to different degrees.