Topological Detection of Information Leakage in Open Quantum Channels: A Deterministic Framework via Nonlinear Dynamics

Quantum Key Distribution (QKD) provides unconditional security guaranteed by the laws of quantum mechanics. However, practical implementations remain vulnerable to physical-layer intrusions, such as the Photon-Number-Splitting (PNS) attack, which exploits non-ideal multi-photon emissions. Current countermeasures heavily rely on asymptotic statistical error bounds or complex optical hardware, introducing inherent detection latency. Building upon our foundational theoretical framework of fractal-entropic scaling, we introduce a protocol-agnostic, deterministic detection framework grounded in the dynamics of open quantum systems. We establish an operational isomorphism between the purity loss (ΔSL) induced by an eavesdropper and the topological symmetry breaking of nonlinear dynamic systems in the complex plane. By mapping discretized stochastic noise into a generalized complex iterative map, microscopic quantum perturbations are non-linearly amplified, forcing an orbital divergence in finite time. Hardware validation via fixed-point arithmetic on a Field-Programmable Gate Array (FPGA) demonstrates real-time, Layer-1 intrusion detection without relying on ideal quantum measurements. Using the BB84 protocol as a canonical case study, we prove that active quantum eavesdropping is topologically incompatible with the continuous natural noise of a secure channel.