  Many quantum systems may have the same classical limit. We argue that in the
classical limit their traces do not necessarily converge one to another. The
trace formula allows to express quantum traces by means of classical quantities
as sums over periodic orbits of the classical system. To explain the lack of
convergence of the traces we need the quantum corrections to the classical
actions of periodic orbits. The four versions of the quantum baker map on the
sphere serve as an illustration of this problem.
