Robust Causal Directionality Inference in Quantum Inference under MNAR Observation and High-Dimensional Noise

In quantum mechanics, observation actively shapes the system, paralleling the statistical notion of Missing Not At Random (MNAR). This study introduces a unified framework for \textbf{robust causal directionality inference} in quantum engineering, determining whether relations are system$\to$observation, observation$\to$system, or bidirectional. The method integrates CVAE-based latent constraints, MNAR-aware selection models, GEE-stabilized regression, penalized empirical likelihood, and Bayesian optimization. It jointly addresses quantum and classical noise while uncovering causal directionality, with theoretical guarantees for double robustness, perturbation stability, and oracle inequalities. Simulation and real-data analyses (TCGA gene expression, proteomics) show that the proposed MNAR-stabilized CVAE+GEE+AIPW+PEL framework achieves lower bias and variance, near-nominal coverage, and superior quantum-specific diagnostics. This establishes robust causal directionality inference as a key methodological advance for reliable quantum engineering.