Accurate and early detection of bone cancer is critical for improving patient outcomes, yet conventional radiographic interpretation remains limited by subjectivity and variability. Conventional AI models often struggle with complex multi-modal noise distributions, non-convex and topologically entangled latent manifolds, extreme class imbalance in rare oncological conditions, and heterogeneous data fusion constraints. To address these challenges, we present a Quantum-Inspired Classical Convolutional Neural Network (QC-CNN) inspired by quantum analogies for automated bone cancer detection in radiographic images. The proposed architecture integrates classical convolutional layers for hierarchical feature extraction with a classical variational layer motivated by high-dimensional Hilbert space analogies for enhanced pattern discrimination. A curated and annotated dataset of bone X-ray images was utilized, partitioned into training, validation, and independent test cohorts. The QC-CNN was optimized using stochastic gradient descent (SGD) with adaptive learning rate scheduling, and regularization strategies were applied to mitigate overfitting. Quantitative evaluation demonstrated superior diagnostic performance, achieving high accuracy, precision, recall, F1-score, and area under the receiver operating characteristic curve (AUC). Results highlight the ability of classical CNN with quantum-inspired design to capture non-linear correlations and subtle radiographic biomarkers that classical CNNs may overlook. This study establishes QC-CNN as a promising framework for quantum-analogy motivated medical image analysis, providing evidence of its utility in oncology and underscoring its potential for translation into clinical decision-support systems for early bone cancer diagnosis. All computations in the present study are performed using classical algorithms, with quantum-inspired concepts serving as a conceptual framework for model design and motivating future extensions.

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.