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arXiv · 1705.01374

Bounds for fidelity of semiclassical Lagrangian states in K{ä}hler quantization

Yohann Le Floch
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Abstract

We define mixed states associated with submanifolds with probability densities in quantizable closed K{ä}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.

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Yohann Le Floch. 2018-03-21. Bounds for fidelity of semiclassical Lagrangian states in K{ä}hler quantization. https://doi.org/10.1063/1.5030410

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