Fractal–Entropic Scaling: A Geometric Encoding of Purity Loss in Open Quantum Systems
Rogerio Junior
AbstractWe investigate linear entropy as an operational witnessof side-channel information in open quantum systems andquantum communication channels. Using the Stinespringdilation framework, we establish that any nontrivial information acquired by an external observer necessarily induces mixedness in suitable probe states received by thelegitimate party. This disturbance is quantified throughlinear entropy and bounded in terms of adversarial distinguishability via standard fidelity and trace-distance inequalities. We further connect these relations to modelindependent constraints arising from entropic uncertaintyin conjugate bases.We present an experimentally accessible estimationscheme based on SWAP tests, providing finite-sample confidence intervals for purity loss without full quantum statetomography. Building on this foundation, we demonstrate that mapping this entropic scalar onto the parameter space of critical quadratic dynamics induces a topological phase transition. This geometric encoding acts as acritical amplifier, transforming subtle entropic deviationsinto macroscopic, structured topological signatures of associated Julia sets. Numerical analysis across distinct decoherence channels reveals a persistent monotonic dependence between fractal dimension and linear entropy, yielding a highly sensitive geometric signature of decoherence.This framework emerged from the development ofan engineering-driven monitoring architecture—a FractalQuantum Sentinel—designed to detect purity degradationin real time. Taken together, our results establish linearentropy as a robust witness of environmental informationgain and demonstrate how its geometric encoding leverages complex dynamics to amplify and expose quantumpurity loss.Keywords: Open Quantum Systems, Linear Entropy,SWAP Test, Entropic Uncertainty, Fractal Geometry, Julia Sets, Quantum Communication.
•Feb 19, 2026•0 citations