QUANTUM INFORMATION METHODS FOR ENTANGLEMENT COMPUTATION: THE CASE OF THE HELIUM ATOM.

The thesis aims to study the applicability of techniques of Quantum Information theory to complex systems, like molecules and biomolecules. Recently, concepts of Quantum Information theory have been applied to the study of phenomena involving molecules, for instance the interaction light-biomolecules. In particular, the entanglement has been proposed to quantify the non-classicality of interactions. The computation of molecular structures and interactions, on the other hand, has been studied for decades mainly to understand reactions’ kinetic and energetic characteristics. It is not straightforward to apply these methods to the computation of quantum correlations. We have therefore explored the computability of such effects using Quantum Information techniques. We started with the study of the electronic correlations in the Helium atom, that is the simplest non trivial case, in order to evaluate the computational problems and to develop approximate methods suitable to more complex systems. We start recalling the definition and basic properties of entanglement, as it is considered in Quantum Information theory. We illustrate how it can be measured and the difficulties one encounters when identical particles are involved, then we concentrate on the case of Helium in particular. In order to study the entanglement in Helium, we treat separately the singlet and the triplet configurations. The method we use consists in computing the reduced density matrix and then the entropy. The possible choices of coordinates, basis functions and computation strategies are discussed, together with their impact on the algorithms. The reduced, single-electron von Neumann and linear entropy for several low-energy eigenstates of Helium are computed by means of a simple configuration-interaction variational method.