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    Coherent states and entropy

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    Let HkH_k, k∈Nk\in {\mathbb{N}}, be the Hilbert spaces of geometric quantization on a K\"ahler manifold MM. With two points in MM we associate a Bell-type state bk∈HkβŠ—Hkb_k \in H_k\otimes H_k. When MM is compact or when MM is Cn{\mathbb{C}}^n, we provide positive lower bounds for the entanglement entropy of bkb_k (asymptotic in kk, as kβ†’βˆžk\to\infty).Comment: Proc. Geom. Sci. Inf. Conf. (Saint-Malo, France, 2023), Lecture Notes Comp. Sci., 14071, Springer, 2023, pp. 516-52
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