Gaussian States: From Classical to Quantum

Gaussian distributions and Gaussian states are fundamental and ubiquitous in probability theory and quantum theory. In this talk, we first present an overview of Gaussian states from both classical and quantum perspectives, then we report a novel physical characterization of Gaussian states in quantum theory: Gaussian states coincide with the minimum uncertainty states for an information-theoretic refinement of the conventional Heisenberg uncertainty relation established in [S. Luo, Phys. Rev. A, 72, 042110 (2005)]. This characterization sheds alternative insights into the nature of Gaussian states. Related open issues concerning discrete analogues of Gaussian states are discussed.