2026-10-26 · arXiv Quantum Physics
arXiv:2610.32428v1 Announce Type: new
Abstract: Quantum secret sharing (QSS) schemes can be constructed from quantum error-correcting codes, but characterizing their access structures and implementation costs becomes challenging for finite-length, high-rate quantum low-density parity-check (qLDPC) codes. We develop an exact computational framework for QSS induced by CSS qLDPC codes. The framework characterizes authorized, forbidden, and intermediate coalitions using restricted parity-check matrices and binary linear algebra, and introduces the accessible logical dimension \(\kappa(A)\), defined through the symplectic rank of locally supported logical classes, to refine the characterization of intermediate coalitions. We further incorporate physical network constraints through separate Tanner-incidence, Steiner-routing, and scheduling-depth costs, and treat the partitioning of physical qubits into participants as an explicit design variable. Numerical experiments on four CSS qLDPC codes verify the predicted complement duality and monotonicity properties and show substantial variation in access transitions and network costs. For the codes studied, the bivariate bicycle instance exhibits the sharpest transition, while network embedding costs vary by more than an order of magnitude across physical topologies. We also show that participant partitioning can substantially improve block-level security and reconstruction thresholds. These results provide a practical bridge between the algebraic structure of CSS qLDPC codes, the graded accessibility of quantum secrets, and the physical constraints of networked QSS implementations.
原文链接：https://arxiv.org/abs/2610.32428
查看更多资讯请见 AI 行业资讯。