On critical points of the objective functional for maximization of qubit observables

We study unconstrained control of a two-level quantum system and analyse critical points of the objective functional which represents quantum average of system observable at some final time $T$. In Proc. Steklov Inst. Math. 285, 233-240 (2014) it was shown that all maxima and minima of the objective functional are global if $T\ge \pi$ (in suitable units). In the present work we show that all maxima and minima are global as soon as $T\ge \pi/2$. Hence we reduce by the factor of two the minimal time for which traps, i.e., local but not global maxima or minima of the objective functional, do not exist.