Nonlocality, evidenced by the violation of Bell inequalities, not only signifies entanglement but also highlights measurement incompatibility in quantum systems. Utilizing the generalized Clauser-Horne-Shimony-Holt (CHSH) Bell inequality, our high-efficiency optical setup achieves a loophole-free violation of 2.0132. This result provides a device-independent lower bound on entanglement, quantified as the entanglement... Show more