Information Preservation in Communication-Constrained Neural Representation Transfer: Classical and Quantum-Inspired Amplitude Encoding

Neural representations learned by neural networks encode task-relevant information, but their behavior under communication constraints is still poorly understood. We propose an information-theoretic framework for the comparison of classical compression and quantum-inspired amplitude encoding for the transfer of representations under controlled dimensional constraints. We analyze frozen intermediate features extracted from a pretrained ResNet-50 on the ImageNet-1K validation set at different depths in the network. The classical pipeline performs rate-controlled dimensionality reduction and uniform quantization, while the quantum-inspired pipeline does amplitude encoding and computational-basis probability decoding without variational circuits or trainable quantum parameters. Quality of representation was evaluated using differential entropy and a decoder-based lower bound on mutual information. Classical compression achieves higher decoder-based mutual information lower bounds at moderate and high communication budgets. However, the quantum-inspired pipeline retained a larger fraction of decoder-extractable task-relevant information under severe dimensional compression, with resource-normalized information efficiency providing a complementary perspective to the substantially higher absolute decoder-based mutual information lower bounds of the classical pipeline. Robustness analyses with qubit reduction and physically motivated noise models showed predictable degradation. Ablation and SHAP analyses indicate that task-relevant information is structured within representational subspaces. These findings support quantum-inspired representation transfer as a framework for studying communication-efficient neural representation transfer under low-bandwidth constraints.