2025/10/09 by Xuhong Liu, Shuai Shao, Liu, Xuhong +1
Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2510.07753
openalex publication_date 2025/10/09 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28
We study the connection between quantum secret sharing (QSS) schemes and k-uniform states of qubits beyond the equivalence between threshold QSS schemes and AME states. Specifically, we focus on homogeneous access structures and show that 3-uniformity is a necessary but not sufficient condition for constructing a 3-homogeneous QSS scheme using states of qubits. This gives a novel connection between non-threshold QSS schemes and k-uniform states. As an application of our result, we classify QSS schemes for up to 7 players and provide explicit characterizations of their existence. Our results offer new insights into the role of k-uniform states in the design of QSS schemes (not necessarily threshold) and provide a foundation for future classifications of QSS schemes with more complex structures.