Current theme: Integrable systems
Mathematics
On the notions of mixed Gaussian quantum states and density operators
byMaurice de Gosson
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.