Quantum Secret Sharing from CSS qLDPC Codes: Computable Access Structures, Accessible Logical Dimension, and Topology-Aware Network Cost

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.