A Characterization of Quantum Gaussian States in Terms of Annihilation Moments

TL;DR

This paper rigorously defines moments of unbounded observables in quantum states and characterizes Gaussian states using annihilation moments, providing precise formulas for their mean and covariance.

Contribution

It introduces a rigorous framework for moments of unbounded observables and characterizes Gaussian states via annihilation moments, with explicit formulas for key state parameters.

Findings

Rigorous definition of moments for unbounded observables.

Characterization of Gaussian states through annihilation moments.

Explicit formulas for mean vector and covariance matrix.

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.