Pattern Based Quantum Key Distribution using the five qubit perfect code for eavesdropper detection

Abstract

I propose a novel quantum key distribution (QKD) protocol securing channels at the physical layer via five-qubit quantum error-correcting codes. By pre-sharing hidden weight-3 to 5 Pauli error patterns, mismatched decoding triggers uncorrectable multi-qubit errors. This framework eliminates intensive classical privacy amplification. Crucially, I provide a formal security proof based on first-principles stabilizer properties. Because uncorrected physical errors project logical measurements onto a mixed state, an eavesdropper encounters a flat 50-50 uniform noise distribution. By mapping interception vectors into a sequential guessing problem over 16 degenerate syndrome configurations, Eve's expected operational mutual information strictly collapses to 0.5093. This quantitative upper bound establishes that any tactical advantage over a blind coin toss is mathematically negligible, ensuring unconditional security during transit while maintaining distinct error signatures under channel noise.