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

Abstract

Continuous variable quantum secret sharing protocol can guarantee the unconditional security of secret key information based on the fundamental laws of physics. However, the state preparation operation may become non-ideal and imperfect in practical continuous variable quantum secret sharing scheme, which will introduce additional excess noise and affect the security of the scheme. Therefore, it is necessary to analyze it. We propose a 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 state preparation performed by any user is equivalent to the corresponding untrusted third party using a phase insensitive amplifier to amplify the ideal modulator and laser owned by the user. The equivalent excess noise introduced by the imperfect state preparation can be calculated comprehensively and quantitatively through the gain of the corresponding phase insensitive amplifier. The results show that the continuous variable quantum secret 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 excess noise tolerance for the imperfect state preparation is achieved by using the specific gain formula of the phase insensitive 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 rate curves can be obtained by the proposed scheme than those by the ideal continuous variable quantum secret sharing protocol. These results indicate that the proposed scheme can improve the practical security of continuous variable quantum secret sharing scheme, and provide a theoretical basis for its practical applications.