Quantum Information Theoretical Analysis of Quantum Secret Sharing

Quantum secret sharing (QSS) schemes are analyzed from an information theoretical perspective centered on the Araki–Lieb inequality. Based on this inequality, mathematical characterizations of QSS schemes and quantum error-correcting codes (QECCs) are given. Furthermore, we present a proof of the relation between QSS schemes and QECCs. This information theoretic description of QSS schemes is used to derive the quantum Singleton bound.