Research On Einsiein-podolsky-rosen Steering For Non-gaussian States

In recent years,the quantum computation and the quantum information science have been rapidly developing,which have attracted lots of attention in academic and engineering fields because of their potential theoretical significance and value of application.Like quantum discrete-variable systems,quantum continuous-variable systems have been developing quickly.For quantum continuous-variable systems,how to perform the transition from Gaussian states to non-Gaussian states is the focus of the academic area.Recently,our knowledge of quantum effect is expanded from the "entanglement" and the "Bell-nonlocality" to the "steering" and the knowledge of resources of the quantum information is accordingly expanded.This paper studies the steering of non-Gaussian states in quantum continuous-variable systems,based on the moment matrices criterion and the entropy inequalities criterion,respectively.The specific research contents are as follows:we adopt moment matrices criterion to calculate the steering of non-Gaussian quantum states.Firstly,we show that moment matrices are superior to Clauser-Home-Shimony-Holt(CHSH)inequalities when applied to Inept states.Next,we use the criterion based on moment matrices to calculate the steering of non-Gaussian states.In particular,we deal with two mode squeezed vacuum thermal mixed states,the mixed photon squeezed vacuum subtracted states in Fock space and the mixed photon squeezed vacuum added states in Fock space.The steering range of these non-Gaussian states are obtained,respectively.It is validated that the moment matrices criterion behave useful for the calculation of the steering of high-order non-Gaussian states.we study the steering of non-Gaussian states based on entropy inequalities.Firstly,we get the Wigner functions of the two mode squeezed vacuum subtracted states in Fock space.Next,based on the Wigner functions and entropy inequalities,we can get the condition of the steering of the two mode squeezed vacuum subtracted states and get the steering range of these non-Gaussian states.Finally,for two mode squeezed vacuum subtracted states,we make a comparison between their steering derived based on moment matrices criterion and that derived based on entropy inequalities criterion.