When Does Fuzzy Adaptation Earn Its Complexity? A Calibration-Aware Computational Study of Finite-Shot Entanglement Detection

Abstract Finite-shot entanglement detection requires measurement resources to be distributed across observable settings while balancing detection power, estimation error, and false-positive control. This study presents a comparative computational evaluation of three measurement-allocation strategies: fixed allocation, variance-adaptive allocation, and a fuzzy-adaptive strategy that combines weighted fuzzy membership scores with variance-based allocation. The methods are evaluated for a two-qubit Werner-type state family using a total budget of 3,000 measurement shots across four simulated detector conditions: ideal operation, fixed offset, uncertain calibration, and drift. The fuzzy strategy is selected from a prespecified family of 81 configurations using development-set detection power and evaluated on separate validation and test samples. The results indicate that the relative performance of the allocation strategies depends on detector conditions and evaluation criteria. Detection power is high under ideal and fixed-offset conditions for all three methods, while uncertain calibration and drift are associated with reduced performance. Fuzzy adaptation achieves the highest observed detection power under uncertain calibration (98.59%) and drift (96.39%), but does not consistently minimize estimation error. Independent boundary-state validation also reveals imperfect false-positive-rate control: the fuzzy strategy exhibits a false-positive rate of 9.0% under uncertain calibration, exceeding the nominal 5% target. These findings demonstrate that apparent gains in detection power must be interpreted alongside false-positive behaviour and estimation accuracy. Because the analysis is computational and the configurations are selected using development-set performance, the results do not establish universal superiority or statistical significance of fuzzy adaptation. Instead, the study provides a condition-dependent benchmark of fuzzy-assisted measurement allocation and identifies calibration robustness and threshold control as important directions for further investigation.