Bell’s inequality with biased experimental settings

We analyse the efficiency of nonlocal correlations in comparison with classical correlations under biased experimental set-up, e.g. for a nonlocal game or a class of Bell-CHSH inequality where both Alice and Bob choose their measurements with a certain bias. We demonstrate that the quantum theory offers advantages over classical theory for the whole range of biasing parameters except for the limiting cases. Moreover, by using fine-grained uncertainty relations to distinguish between classical, quantum and superquantum correlations, we further confirm the underlined advantage of quantum correlations over classical correlations. Our results clearly show that all pure bi-partite entangled states violate the Bell-CHSH inequality under biased set-up. Although for the two-qubit mixed Werner state, the Horodecki state and a state proposed by Ma et al. (Phys Lett A 379:2802, 2015) the range of violation is same in both biased and unbiased scenarios, the extent of violation is different in both cases. We extend our analysis to detect nonlocal correlations using quantum Fisher information and demonstrate a necessary condition for capturing nonlocality in biased scenario. Furthermore, we also describe properties of nonlocal correlations under noisy conditions considering a biased experimental set-up.