Baek, Kyunghyun Ryu, Junghee Lee, Jinhyoung 2025-05-22T06:30:24Z 2025-05-22T06:30:24Z 2025-05-21 2025-05 1367-2630 https://pubs.kist.re.kr/handle/201004/152487 We suggest generalized robustness for quantifying nonlocality and derive its equivalence to the maximum violation ratio of Bell inequalities defined as vectors with non-negative elements. We investigate its properties by comparing it with white-noise and standard robustness measures. As a result, we show that white-noise robustness does not fulfill monotonicity under local operations and shared randomness, whereas the other measures do. To compare the standard and generalized robustness measures, we introduce the concept of inequivalence, which indicates a reversal in the order relationship depending on the choice of monotones. From an operational perspective, the inequivalence of monotones for resourceful objects implies the absence of free operations that connect them. Applying this concept, we find that standard and generalized robustness measures are inequivalent between even- and odd-dimensional cases up to eight dimensions. This is obtained using randomly performed Collins-Gisin-Linden-Massar-Popescu measurement settings in a maximally entangled state. This study contributes to the resource theory of nonlocality and sheds light on comparing monotones by using the concept of inequivalence valid for all resource theories. English Institute of Physics Publishing Robustness measures for quantifying nonlocality Article 10.1088/1367-2630/adcd5a 1 New Journal of Physics, v.27, no.5 New Journal of Physics 27 5 Y scie scopus 001480305100001 2-s2.0-105004174762 Physics, Multidisciplinary Physics Article HIDDEN-VARIABLES ORDERING STATES ENTANGLEMENT resource theory nonlocality local operations and shared randomness