Geometric Entanglement of Symmetric States and the Majorana Representation

Permutation-symmetric quantum states appear in a variety of physical situations, and they have been proposed for quantum information tasks. This article builds upon the results of [New J. Phys. 12, 073025 (2010)], where the maximally entangled symmetric states of up to twelve qubits were explored, and their amount of geometric entanglement determined by numeric and analytic means. For this the Majorana representation, a generalization of the Bloch sphere representation, can be employed to represent symmetric n qubit states by n points on the surface of a unit sphere. Symmetries of this point distribution simplify the determination of the entanglement, and enable the study of quantum states in novel ways. Here it is shown that the duality relationship of Platonic solids has a counterpart in the Majorana representation, and that in general maximally entangled symmetric states neither correspond to anticoherent spin states nor to spherical designs. The usability of symmetric states as resources for measurement-based quantum computing is also discussed.Comment: 10 pages, 8 figures; submitted to Lecture Notes in Computer Science (LNCS

On the origin of influenza A hemagglutinin

Recent advances in phylogenetic methods have produced some reassessments of the ages of the most recent common ancestor of hemagglutinin proteins in known strains of influenza A. This paper applies Bayesian phylogenetic analysis implemented in BEAST to date the nodes on the influenza A hemagglutinin tree. The most recent common ancestor (MRCA) of influenza A hemagglutinin proteins is located with 95% confidence between 517 and 1497 of the Common Era (AD), with the center of the probability distribution at 1056 AD. The implications of this revised dating for both historical and current epidemiology are discussed. Influenza A can be seen as an emerging disease of mediaeval and early modern times