Measurement Incompatibility vs. Bell Non-locality: An Approach via Tensor Norms

Explore the intricate relationship between measurement incompatibility and quantum non-locality in this hour-long lecture from the Thematic Programme on "Tensor Networks: Mathematical Structures and Novel Algorithms" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the analysis of Bell inequalities, examining when measurement incompatibility alone is sufficient to guarantee a quantum violation. Investigate the comparison of two tensor norms on the space of dichotomic quantum measurements, one characterizing measurement compatibility and the other describing violations of Bell inequalities. Discover the sufficient conditions for the equivalence of these two concepts in terms of the correlation Bell inequality matrix. Learn why the CHSH inequality and its variants stand out as the only ones satisfying these conditions, gaining deeper insights into the fundamental aspects of quantum theory and their mathematical representations.