Motivated by device-independent quantum information protocols, we study a class of marginal-free asymmetric Clauser-Horne-Shimony-Holt (CHSH) expressions in which Alice's two measurement settings carry different weights. For $0<\alpha \le 1$, within the two-qubit projective-measurement model, we derive a tight analytic lower bound on the concurrence of arbitrary two-qubit states compatible with an observed asymmetric CHSH value. We then combine this entanglement-certification result with established entropic-uncertainty, convexification, and Gauss-Radau–Navascués-Pironio-Acín semidefinite-programming techniques to obtain finite-level lower-bound estimates on the conditional von Neumann entropy $H\left(A_0\right|E)$. Finally, within the same finite-level semidefinite-programming setting, we compare the entropy estimates obtained from asymmetric and standard CHSH expressions under white-noise and finite-detection-efficiency models. The results indicate that mildly asymmetric choices of $\alpha$ can give more favorable finite-level estimates of the visibility and detection-efficiency thresholds in selected regimes of the models considered here.

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• Quantum correlations, foundations & formalism
• Quantum cryptography
• Quantum information theory