Quantum correlations and geometry

Quantum systems exhibit correlations which are in some sense stronger than correlations in classical stochastic processes and lead to the violation of the Bell inequalities. These quantum correlations are at the origin of the better efficiencies of quantum computers as compared to classical computers to solve certain tasks. For composite systems in a pure state (given by a wave function), quantum correlations always arise from entanglement. In contrast, for mixed states (given by density matrices), most states with no entanglement are quantum correlated. Such states are characterized by the positivity of a quantity called the quantum discord. In this talk, we will review these concepts and present a geometrical approach to quantum correlations based on the Bures distance on the set of quantum states. This distance coincides with the Fubiny-Study distance for pure states and is a quantum analog to the statistical distance between probability measures.