Structured Correlation Levels After Partial Time Reversal in Small-Scale Quantum Systems

We analyse how mutual information and correlation structure differ between structured and randomised quantum systems under a partial time-reversal protocol. Structured correlations—defined as non-random patterns in mutual information between subsystems—arise in complex systems across physical, biological, and computational domains. Understanding how such structures behave under perturbation remains an open question with implications for theories of emergence. Analogous questions arise in artificial systems, where large language models and neural networks exhibit emergent structures that persist through training dynamics; however, the mechanisms underlying such persistence remain poorly characterised. This paper investigates post-interference correlation levels in small-scale quantum circuits (5-15 qubits) as a minimal, controllable testbed. We compare mutual information between circuits initialised with structured entanglement patterns and randomised baseline circuits subjected to identical local interference protocols. Using mutual information retention metrics and statistical comparison, we quantify the degree to which structured initial conditions exhibit differential correlation levels relative to unstructured controls. Results indicate that structured circuits retain significantly higher absolute mutual information following local interference compared to randomised counterparts (8.0 vs 4.2 bits, z = 3.50, p < 0.001), with this differential arising from initial conditions rather than differential dynamical response. Accordingly, we distinguish between the preservation of initial correlation magnitude under local operations and active resistance to correlation-destroying perturbations. We emphasise that these findings do not support claims of consciousness, intelligence, or agency in quantum systems. The contribution of this work is strictly methodological: we establish operational definitions, reproducible experimental protocols, and quantitative metrics for studying structured correlation levels under local interference. Keywords:Mutual information, Entropy dynamics, Quantum correlations, Structure persistence, Interference protocols, Emergence in complex systems, Information-theoretic metrics