Construction of a Class of Communication-Efficient Quantum Secret Sharing Schemes

Quantum secret sharing is a fundamental technique in quantum cryptography. However, in practical quantum networks, it still faces several bottlenecks, such as high quantum communication cost and low transmission efficiency. To reduce the communication cost, ramp quantum secret sharing schemes have been proposed in existing studies. Nevertheless, intermediate sets in such schemes may leak partial information about the secret. To address this problem, we develop a sufficient linear-algebraic criterion for such leakage, via a reduced channel and a secret-reference mutual-information witness; for ECSS, an explicit condition follows from a Vandermonde-type LU decomposition. We then propose a perfect-secrecy lifting of that communication-efficient ECSS construction, agnostic to the leakage form: the data-reconstruction structure and its d-participant cost are retained, while leakage is removed by a hybrid classical key layer. The information-theoretic secrecy statement is proved for the stated pre-announced reconstruction-set model. The channel-disturbance checks are treated as implementation-level auxiliary safeguards, not as part of the secrecy proof. The distribution-phase saving is model-dependent, whereas the data-reconstruction saving is not. We report intrinsic quantum communication, classical key-sharing, and storage resources under a common accounting convention, while auxiliary channel-checking overhead is reported separately for the proposed implementation.