Contextual Quantum Entropic Lattices for Non-Clifford Information Propagation: A Theoretical Framework for Ultra-Secure Qubit Channels

This paper introduces a new class of quantum information structures called entropic lattices, designed to encode and propagate information using non-Clifford operations in contextual quantum frameworks. Motivated by the limitations of classical error correction and the need for ultra-secure quantum communication, we develop a purely theoretical and rigorous approach to model entropic interactions between qubits across lattice sites. Our framework leverages contextuality—a uniquely quantum phenomenon—as a resource to enable controlled information flow beyond stabilizer limitations. We construct an algebraic basis for entropic channels and derive propagation laws under entropy-preserving, non-Clifford logic. The proposed model is built entirely from first principles, includes high-level mathematical formalism, and does not rely on any experimental data. This work aims to establish a new foundation for robust, theoretically-grounded quantum communication protocols that extend the scope of quantum error resistance and computational universality.