Mixed state, entanglement measure

The first two measures are also called operational measures, while the second two don t admit a direct operational interpretation in terms of entanglement manipulations. Suppose is a measure defined on mixed states that satisfy the conditions for a good measure mentioned above. Then we can prove that for all states p e H ), Eo p) < E p) < Ec p), and both Eo p) and Ec p) coincide on pure states with the von Neumann reduced entropy as demonstrated earlier. 

At the current time, there is no simple way to carry out the calculations with all these entanglement measures. Their properties, such as additivity, convexity, and continuity, and relationships are still under active investigation. Even for the best-understood entanglement of formation of the mixed states in bipartite systems AB, once the dimension or A or B is three or above, we don t know how to express it simply, although we have the general definitions given previously. However, for the case where both subsystems A and B are spin-i particles, there exists a simple formula from which the entanglement of formation can be calculated [42]. 

In this case the entanglement of formation is given in terms of another entanglement measure, the concurrence C [42-44]. The entanglement of formation varies monotonically with the concurrence. From the density matrix of the two-spin mixed states, the concurrence can be calculated as follows ... 

---