Optimal entanglement witnesses based on local orthogonal observables

We show that the entanglement witnesses based on local orthogonal observables, which were introduced by Yu and Liu [Phys. Rev. Lett. 95, 150504 (2005)] and Guhne [Phys. Rev. A 74, 010301(R) (2006)] in linear and nonlinear forms, respectively, can be optimized. As applications, we use our method to calculate the optimal nonlinear witnesses of pure bipartite states and to show a lower bound on the I concurrence of bipartite higher-dimensional systems.