Dynamic Verifiable Quantum Secret Sharing with Error Correction and Formal Security Guarantees

This paper integrates dynamic participant management, verifiable secret reconstruction, and fault tolerance against noise and adversarial attacks. By leveraging graph states for scalable entanglement and a quantum error-correcting code (\([\![n,1,d]\!]\)), the protocol enables secure sharing of classical and quantum secrets among n participants, requiring a threshold k for reconstruction. A hybrid verification mechanism---combining randomly interleaved trap qubits and post-quantum hash functions---detects malicious behavior with probability \(1 - \left(\frac{3}{4}\right)^m\) for m traps, while dynamic graph-state reconfiguration permits seamless participant addition/removal. Formal security proofs demonstrate information-theoretic secrecy against collusion ( t < k participants), adaptive coherent attacks, and revoked dishonest participants, alongside tolerance for \(t = \lfloor (d-1)/2 \rfloor\) errors. The protocol’s composable security is established via the Universal Composability framework, and simulations on IBM Quantum achieve greater than 95\% secret recovery fidelity under depolarizing noise ((p = 0.01). Key innovations include linear resource scaling, stabilizer-based error correction, and compatibility with post-quantum cryptography. This work bridges theoretical security with practical feasibility, offering a robust framework for quantum-secure systems in dynamic, noisy environments.