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We propose to quantify the entanglement of pure states of $N \times N$bipartite quantum system by defining its Husimi distribution with respect to$SU(N)\times SU(N)$ coherent states. The Wehrl entropy is minimal if and onlyif the pure state analyzed is separable. The excess of the Wehrl entropy isshown to be equal to the subentropy of the mixed state obtained by partialtrace of the bipartite pure state. This quantity, as well as the generalized(R{\'e}nyi) subentropies, are proved to be Schur--convex, so they areentanglement monotones and may be used as alternative measures of entanglement

Wehrl entropy, Lieb conjecture, and entanglement monotones