Bounds of concurrence and their relation with fidelity and frontier states

The bounds of concurrence in [F. Mintert, A. Buchleitner, Phys. Rev. Lett. 98 (2007) 140505] and [C. Zhang, et al., Phys. Rev. A 78 (2008) 042308] are proved by using two properties of the fidelity. In two-qubit systems, for a given value of concurrence, the states achieving the maximal upper bound, the minimal lower bound or the maximal difference upper–lower bound are determined analytically.