Abstract
One cornerstone of quantum mechanics is the notion of mixed quantum state. In this talk, we will give a mathematically rigorous definition of this concept and of the associated notion of density operator from the point of view of harmonic analysis and symplectic geometry. We will discuss in detail the case of so-called gaussian states which play a major role in the applications to quantum information and optics.
Keywords
Density operator, symplectic geometry, Gaussian symbols, trace class operators.