A Characterization of Quantum Gaussian States in Terms of Annihilation Moments
arXiv:2111.06570 · doi:10.1016/S0034-4877(22)00081-7
Abstract
We give a rigorous definition of moments of an unbounded observable with respect to a quantum state in terms of Yosida's approximations of unbounded generators of contractions semigroups. We use this notion to characterize Gaussian states in terms of annihilation moments. As a by-product, rigorous formulae for the mean value vector and the covariance matrix of a Gaussian state are obtained.