Improving fidelity of quantum secret sharing by weak measurement

Quantum secret sharing is an important branch of quantum cryptography. In this paper, we firstly propose a simple four-party quantum secret sharing scheme with entangled states. Since the noisy channel has a great influence on the shared quantum secret, we analyze the impact of the noisy channel on quantum secret sharing and obtain the expression among the fidelity, noisy coefficient and shared quantum state coefficients. To enhance the fidelity of the shared secret, we use the weak measurement method to protect the scheme in noisy environment. Furthermore, we analyze the fidelity between the obtained secret and the initial one after the amplitude damped channel. Finally, we take the concrete quantum state as an example to compare with the original way and find that the weak measurement method has a certain significance to improve the fidelity of the secret state in the scheme.