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We define mixed states associated with submanifolds with probabilitydensities in quantizable closed K{\"a}hler manifolds. Then, we address theproblem of comparing two such states via their fidelity. Firstly, we estimatethe sub-fidelity and super-fidelity of two such states, giving lower and upperbounds for their fidelity, when the underlying submanifolds are two Lagrangiansubmanifolds intersecting transversally at a finite number of points, in thesemiclassical limit. Secondly, we investigate a family of examples on thesphere, for which we manage to obtain a better upper bound for the fidelity. Weconclude by stating a conjecture regarding the fidelity in the general case.

Bounds for fidelity of semiclassical Lagrangian states in K{\"a}hler quantization