  We define mixed states associated with submanifolds with probability
densities in quantizable closed K{\"a}hler manifolds. Then, we address the
problem of comparing two such states via their fidelity. Firstly, we estimate
the sub-fidelity and super-fidelity of two such states, giving lower and upper
bounds for their fidelity, when the underlying submanifolds are two Lagrangian
submanifolds intersecting transversally at a finite number of points, in the
semiclassical limit. Secondly, we investigate a family of examples on the
sphere, for which we manage to obtain a better upper bound for the fidelity. We
conclude by stating a conjecture regarding the fidelity in the general case.
