On a local hidden-variable model for postselected EPR correlations

A theoretical and numerical analysis of a Bell-type experiment is presented, where linear polarization measurements on nonmaximally entangled two-qubit states are modeled through a sigmoid-based threshold mechanism that violates the fair-sampling assumption required by the CHSH inequality. Numerical simulations characterize how closely this local construction can reproduce quantum-like correlations in the postselected detected sample, for both the |Phi_r> and |Psi_r> states over a range of entanglement parameters. For the tested configurations, the model produces CHSH-type violations only in the postselected detected sample through a setting-dependent detection mechanism, operating outside the assumptions of both the CHSH inequality and Mermin’s 82.8% efficiency bound. The model is not in conflict with loophole-free Bell experiments, which specifically close the detection loophole exploited here. The CH–Eberhard analysis in the one-detector-per-side configuration yields throughout the full range of entanglement parameters, as required for a strictly local model. The model is further extended with a local adaptive-threshold mechanism implementing one-sided memory. A paired comparison shows that this specific memory rule produces a systematic and reproducible shift in the CH–Eberhard parameter relative to the fixed-threshold model, while leaving the CH–Eberhard analysis qualitatively unchanged under the tested conditions. The results characterize how a local, setting-dependent postselection mechanism shapes Bell-test statistics across a range of entanglement parameters, within the specific configurations and threshold rules tested.