Practical continuous variable quantum secret sharing schemebased on non-ideal quantum state preparation

Continuous variable quantum secret sharing protocol can guarantee the unconditional security of secret keyinformation based on the fundamental laws of physics. However, the state preparation operation may becomenon-ideal and imperfect in practical continuous variable quantum secret sharing scheme, which will introduceadditional excess noise and affect the security of the scheme. Therefore, it is necessary to analyze it. We proposea practical continuous variable quantum secret sharing protocol based on imperfect state preparation.Specifically, in the proposed scheme, we assume that there are multiple users, and the imperfect statepreparation performed by any user is equivalent to the corresponding untrusted third party using a phaseinsensitive amplifier to amplify the ideal modulator and laser owned by the user. The equivalent excess noiseintroduced by the imperfect state preparation can be calculated comprehensively and quantitatively through thegain of the corresponding phase insensitive amplifier. The results show that the continuous variable quantumsecret sharing scheme is sensitive to the excess noise introduced by the imperfect state preparation operation,which will inevitably reduce its performance and security. Fortunately, the upper bound of the additional excessnoise tolerance for the imperfect state preparation is achieved by using the specific gain formula of the phaseinsensitive amplifier, thus the security risks caused by the imperfect state preparation can be effectively solved.Due to considering the additional excess noise introduced by imperfect state preparation, tighter secret key ratecurves can be obtained by the proposed scheme than those by the ideal continuous variable quantum secretsharing protocol. These results indicate that the proposed scheme can improve the practical security ofcontinuous variable quantum secret sharing scheme, and provide a theoretical basis for its practicalapplications