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Entangled quantum states share properties that do not have classical analogs,in particular, they show correlations that can violate Bell inequalities. It istherefore an interesting question to see what happens to entanglement measures-- such as the entanglement entropy for a pure state -- taking thesemi-classical limit, where the naive expectation is that they may becomesingular or zero. This conclusion is however incorrect. In this paper, wedetermine the $\hbar\rightarrow 0$ limit of the bipartite entanglement entropyfor a one-dimensional system of $N$ quantum particles in an external potentialand we explicitly show that this limit is finite. Moreover, if the particlesare fermionic, we show that the $\hbar\rightarrow 0$ limit of the bipartiteentanglement entropy coincides with the Shannon entropy of $N$ bits.

The $\hbar\rightarrow 0$ Limit of the Entanglement Entropy