Wehrl entropy, Lieb conjecture and entanglement monotones

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 only if the pure state analyzed is separable. The excess of the Wehrl entropy is shown to be equal to the subentropy of the mixed state obtained by partial trace of the bipartite pure state. This quantity, as well as the generalized (R{\'e}nyi) subentropies, are proved to be Schur--convex, so they are entanglement monotones and may be used as alternative measures of entanglement

Interlocked host anion recognition by an indolocarbazole-containing [2]rotaxane

The design, synthesis, structure, and anion-binding properties of the first indolocarbazole-containing interlocked structure are described. The novel [2]rotaxane molecular structure incorporates a neutral indolocarbazole-containing axle component which is encircled by a tetracationic macrocycle functionalized with an isophthalamide anion recognition motif. (1)H NMR and UV-visible spectroscopies and X-ray crystallography demonstrated the importance of pi-donor-acceptor, CH...pi, and electrostatic interactions in the assembly of pseudorotaxanes between the electron-deficient tetracationic macrocycle and a series of pi-electron-rich indolocarbazole derivatives. Subsequent urethane stoppering of one of these complexes afforded a [2]rotaxane, which was shown by (1)H NMR spectroscopic titration experiments to exhibit enhanced chloride and bromide anion recognition compared to its non-interlocked components. Computational molecular dynamics simulations provide further insight into the mechanism and structural nature of the anion recognition process, confirming it to involve cooperative hydrogen-bond donation from both macrocycle and indolocarbazole components of the rotaxane. The observed selectivity of the [2]rotaxane for chloride is interpreted in terms of its unique interlocked binding cavity, defined by the macrocycle isophthalamide and indolocarbazole N-H protons, which is complementary in size and shape to this halide guest