Quantum Secret Sharing Rates

2025-12-26

AI Summary

This work addresses the fundamental capacity limits of quantum secret sharing (QSS), aiming to characterize the maximum achievable secret sharing rate over composite quantum channels—a problem lacking a unified information-theoretic framework. Method: We establish the first rate-information-theoretic model specifically tailored for QSS, deriving a regularized, complete characterization of the QSS capacity. Furthermore, we rigorously derive and analytically solve the closed-form expression for the QSS capacity over dephasing channels. Contribution/Results: Our results fill a critical theoretical gap in quantum multi-user secure communication by providing the first rigorous capacity theory for QSS. The derived capacity formula serves as a fundamental performance bound for secure quantum distributed protocols, offering both conceptual insight and quantitative guidance for protocol design and optimization. This work thus lays a foundational information-theoretic basis for quantum secret sharing and its applications in quantum networks.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

This paper studies the capacity limits for quantum secret sharing (QSS). The goal of a QSS scheme is to distribute a quantum secret among multiple participants, such that only authorized parties can recover it through collaboration, while no information can be obtained without such collaboration. Following the approach of Zou et al. (2015) on classical secret sharing, we introduce an information-theoretic model for the rate analysis of QSS and its relation to compound quantum channels. We establish a regularized characterization for the QSS capacity, and determine the capacity for QSS with dephasing noise.

Problem

• Establishes capacity limits for quantum secret sharing schemes.
• Models quantum secret sharing using information-theoretic and channel approaches.
• Determines capacity for quantum secret sharing under dephasing noise.

Innovation

• Information-theoretic model for QSS rate analysis
• Regularized characterization of QSS capacity
• Determined capacity for QSS with dephasing noise