Robustness And Coherence Of Nonclasslity For Photon-number Superposition States

Nonclassicality is one of the most fundamental characteristics of quantum mechanics and is also a necessary resource for various quantum information processing tasks.Nonclassicality of quantum states is a key issue in quantum resource theory,and the measures of nonclassicality include Bell inequalities,Wigner functions,Husimi Q functions,and robustness measures.Robustness can be used to directly measure the nonclassicality of quantum states,and this method has been widely applied in the field of quantum computing.In previous studies,the robust nonclassicality of single-photon number states has been to some extent understood,but the problem of robust nonclassicality for superposition states composed of vacuum and single-photon states remains unsolved.This article proposes a novel method to address this problem,which can effectively solve the robust nonclassicality problem for superposition states of vacuum and singlephoton states.The research process and main achievements are divided into the following two aspects:(1)Study of superposition states of vacuum and single-photon states: Firstly,the optimal witness is constructed based on the known lower bound formula for the robust nonclassicality of Fock states.Then,numerical calculations are performed to obtain the lower bound of the robust nonclassicality for superposition states of vacuum and single-photon states.The specific numerical values of the upper bound of robustness for attenuated states can be obtained through numerical calculations,and it can be observed that the numerical value of the robust nonclassicality of the superposition states of vacuum and single-photon states is around()∈ [0,2.718].The formula optimizing the upper bound of robust nonclassicality corresponding to the lower bound of robust nonclassicality yields results through numerical calculations,and it can be seen that the coincidence of the upper and lower bounds verifies the robust nonclassicality of the superposition states of vacuum and single-photon states.It is also evident that the robust nonclassicality exhibits linear changes during the process with probability ∈ [0,1].(2)By introducing the decay factor = 0.8,0.6,0.4,0.2 into the target state,the lower bound of the robustness for the attenuated states can be obtained using the lower bound formula of robust nonclassicality.Then,using the definition method of robustness,the upper bound of the robust nonclassicality of the attenuated states is solved,and the upper and lower bounds coincide to a large extent.It can also be observed that the numerical value of the robust nonclassicality of the attenuated states gradually decreases as the noise increases.According to the research results,the robust nonclassicality of the superposition states of vacuum and singlephoton states has been completely resolved.