Theorem on nonclassical states

Abstract

Let the density matrix of an arbitrary state be expressed in terms of number states as \ensuremath{\rho}^=${\ensuremath{\sum}}_{\mathit{n}=0}^{\mathrm{\ensuremath{\infty}}}$${\ensuremath{\sum}}_{\mathit{m}=0}^{\mathrm{\ensuremath{\infty}}}$\ensuremath{\rho}(n,m)\ensuremath{\Vert}n〉〈m mU. We prove the following theorem: If \ensuremath{\rho}(0,0)=0, then the state is as nonclassical as possible according to the measure introduced by Lee [Phys. Rev. A 44, R2775 (1991)].