Maria Alessandra Vaccaro

Bio: Maria Alessandra Vaccaro is an academic researcher from University of Palermo. The author has contributed to research in topics: Conic section & Nine-point conic. The author has an hindex of 2, co-authored 14 publications receiving 18 citations. Previous affiliations of Maria Alessandra Vaccaro include University of Perugia.

Kronecker modules and reductions of a pair of bilinear forms

Abstract: We give a short overview on the subject of canonical reduction of a pair of bilinear forms, each being symmetric or alternating, making use of the classification of pairs of linear mappings between vector spaces given by J. Dieudonné.

François Le Lionnais and the Oulipo. The Unexpected Role of Mathematics in Literature

Abstract: “The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry” (Bertrand Russel, Mysticism and Logic, 1910). This sentence, quoted by Francois Le Lionnais in his work La Beaute en Mathematiques in [1], reflects his conception of a deep bond between mathematics and literature. He had a multifaceted education and was an erudite and founder of the Oulipo with Raymond Queneau. Even though he was neither a ‘professional’ mathematician nor a ‘professional’ man of letters but only an epicurien passionne as he defined himself [2], while alive, he channelled his interests in the theorisation of the so-called litterature potentielle (potential literature) “pour exciter les curieux d’insolite et faire reflechir les passionnes de litterature aussi bien que le fanatiques de mathematiques” [3]. The purpose of this chapter is outline the figure of Francois Le Lionnais (who we will refer to from here on as FLL as he himself liked to do [4]) through the analysis of his most meaningful works, which, in the current literature, appear as subordinated to the works of the more famous and researched Queneau.

The action of a compact Lie group on nilpotent Lie algebras of type {n,2}

Abstract: We classify nite-dimensional real nilpotent Lie algebras with 2-dimensional central commutator ideals admitting a Lie group of automorphisms isomorphic to SO2(R). This is the rst step to extend the class of nilpotent Lie algebras h of typefn; 2g to solvable Lie algebras in which h has codimension one.

Transformations of Stabilizer States in Quantum Networks

Abstract: Stabilizer states and graph states find application in quantum error correction, measurement-based quantum computation and various other concepts in quantum information theory. In this work, we study party-local Clifford (PLC) transformations among stabilizer states. These transformations arise as a physically motivated extension of local operations in quantum networks with access to bipartite entanglement between some of the nodes of the network. First, we show that PLC transformations among graph states are equivalent to a generalization of the well-known local complementation, which describes local Clifford transformations among graph states. Then, we introduce a mathematical framework to study PLC equivalence of stabilizer states, relating it to the classification of tuples of bilinear forms. This framework allows us to study decompositions of stabilizer states into tensor products of indecomposable ones, that is, decompositions into states from the entanglement generating set (EGS). While the EGS is finite up to 3 parties [Bravyi et al., J. Math. Phys. 47, 062106 (2006)], we show that for 4 and more parties it is an infinite set, even when considering party-local unitary transformations. Moreover, we explicitly compute the EGS for 4 parties up to 10 qubits. Finally, we generalize the framework to qudit stabilizer states in prime dimensions not equal to 2, which allows us to show that the decomposition of qudit stabilizer states into states from the EGS is unique.