An exact computational framework for quantum symmetric subspace (QSS) induced by code-switching syndrome (CSS) quasi-cyclic low-density parity-check (qLDPC) codes has been developed. This framework characterizes authorized, forbidden, and intermediate coalitions using restricted parity-check matrices and binary linear algebra. It introduces the accessible logical dimension κ(A), defined through the symplectic rank of locally supported logical classes, to refine the characterisation of intermediate coalitions.

Physical network constraints are further incorporated through separate Tanner-incidence, Steiner-routing, and scheduling-depth costs. The partitioning of physical qubits into participants is treated as an explicit design variable. Numerical experiments validate this approach; Qatar Center for Quantum Computing, College of Science and Engineering, Hamad Bin Khalifa University, Doha, Qatar

Optimised QuBit Partitioning Enables Scalable Quantum Secret Sharing Networks

Quantum secret sharing schemes have seen network embedding costs reduced by more than an order of magnitude through optimised participant partitioning; complex codes formerly made practical implementation impossible due to high communication overhead. The team demonstrates careful allocation of physical qubits among participants sharply improves both block-level security and reconstruction thresholds in CSS qLDPC code implementations. This framework links algebraic properties of these error-correcting codes with access structures, enabling secure information distribution while accounting for real-world constraints like qubit routing and scheduling.

QSS systems can now be tailored to specific topologies by treating the partition of qubits as a key design variable, paving the way for scalable networked quantum cryptography applications. Numerical tests across four distinct CSS qLDPC code types, hypergraph product, bivariate bicycle, and two variations of Hamming codes, confirmed predicted properties such as complement duality and monotonicity in accessibility levels; notably, ‘bivariate bicycle’ showed the most abrupt shift between secure and insecure access. Network embedding costs varied significantly, by more than an order of magnitude, depending on the chosen physical topology for qubit connections.

Analytical links between code structure and communication overhead enable initial assessment

This framework offers detailed computational insight into quantum secret sharing schemes built from CSS qLDPC codes, but current validation relies on analysis of only four specific code types. Proving generalizability beyond these examples remains a challenge, with scaling up to wider ranges of qLDPC structures or sharply increasing qubit counts potentially revealing unforeseen limitations. Despite this limited scope, and acknowledging that more complex quantum error correction designs may pose challenges, it represents a step forward for practical quantum secret sharing; previously assessing abstract mathematical properties alongside real-world network limitations was difficult.

Analysing restricted parity-check matrices using binary linear algebra accurately defines how different groups can access shared secrets within these systems, the team introduced a metric called accessible logical dimension for refined characterisation. A computational tool linking CSS qLDPC code properties to network constraints like connection costs and data routing is now available. This allows researchers to assess the feasibility of secure communication in increasingly complex quantum networks with greater precision.

This research developed a computational framework that characterizes quantum secret sharing schemes built from CSS qLDPC codes by connecting their algebraic structure to practical network limitations. Numerical experiments on four different qLDPC codes demonstrated predictable relationships between accessibility levels and network costs, revealing more than an order of magnitude variation depending on physical topology; the ‘bivariate bicycle’ code exhibited particularly sharp transitions between secure and insecure access. This work provides tools to assess feasibility in complex quantum networks based on both mathematical properties *and* communication overheads.

👉 More information
🗞 Quantum Secret Sharing from CSS qLDPC Codes: Computable Access Structures, Accessible Logical Dimension, and Topology-Aware Network Cost
✍️ Malik Mouaji and Saif Al-Kuwari (Hamad Bin Khalifa University)
🧠 ArXiv: https://arxiv.org/abs/2610.32428

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