Quantum Secret Sharing in Noisy Environment

As an unavoidable factor of real-world implementation of quantum cryptograph, quantum noise severally affects the security and reliability of the quantum system. In this paper, we study how QSS, an important branch of quantum cryptograph, is affected by noise or decoherence. QSS protocols for sharing classical information and quantum states are studied in four types of noise that usually encountered in real-world, i.e., the bit-flip, phase-flip (phase-damping), depolarizing and amplitude-damping noise, respectively. Two methods are introduced to evaluate the effect of noise. For the QSS protocol sharing classical information, the efficiency for generating secret key is used. Our results show that the efficiencies are quiet different from each other in four types of noise. While for the protocol sharing quantum states, the output states and the state-independent average fidelity are studied, respectively. It indicates that the players will get two different output states in the amplitude-damping noise, but get one output state in the other three types of noise. Besides, the state-independent average fidelity behaves differently from each other. Our study will be helpful for analyzing and improving quantum secure communications protocols in real-world.