  By investigating the convex property of the function R, appeared in computing
the entanglement of formation for isotropic states in Phys. Rev. Lett. 85, 2625
(2000), and a tight lower bound of entanglement of formation for arbitrary
bipartite mixed states in Phys. Rev. Lett. 95, 210501 (2005), we show
analytically that the very nice results in these papers are valid not only for
dimensions 2 and 3 but any dimensions.
