Quantitative security analysis of three-level unitary operations in quantum secret sharing without entanglement

Quantum secret sharing (QSS) protocols without entanglement have showed high security by virtue of the characteristics of quantum mechanics. However, it is still a challenge to compare the security of such protocols depending on quantitative security analysis. Based on our previous security analysis work on protocols using single qubits and two-level unitary operations, QSS protocols with single qutrits and three-level unitary operations are considered in this paper. Under the Bell-state attack we propose, the quantitative security analyses according to different three-level unitary operations are provided respectively in the one-step and two-step situations. Finally, important conclusions are drawn for designing and implementing such QSS protocols. The method and results may also contribute to analyze the security of other high-level quantum cryptography schemes based on unitary operations