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Explore the intriguing relationship between coherent states and entropy in this 15-minute conference talk from GSI. Delve into the Hilbert spaces of geometric quantization on Kähler manifolds, examining the entanglement entropy of coherent states. Discover positive lower bounds for entanglement entropy in both compact manifolds and C^n spaces, with a focus on asymptotic behavior as k approaches infinity. Gain insights into the mathematical foundations of quantum information theory and its applications in geometric quantization.