Maximal violation of lifted Bell inequalities, self-testing, and the geometry of the quantum set
Chellasamy Jebarathinam, Jui-Chen Hung, Yeong-Cherng Liang · arXiv (Cornell University) · 2019
In quantum information, lifting is a procedure employed to derive a Bell inequality applicable in a more complicated Bell scenario from an existing one. It is known that the procedure of lifting considered by Pironio [J. Math. Phys. A 46, 062112 (2005)] preserves the facet-defining property of a Bell inequality. Here, we perform a complementary investigation showing that the maximal value of a lifted Bell inequality is preserved for both the set of non-signaling correlations and quantum correlations. Moreover, the optimal quantum state leading to the maximal violation of an outcome-lifted (party-lifted) Bell inequality is provably (essentially) the same as that for the original Bell inequality. The self-testing property of a Bell inequality, however, is only partially preserved through the outcome-lifting procedure as the corresponding maximal quantum violation is achievable with distinct quantum strategies. The implication of such a degeneracy on the geometry of the quantum set of correlations, as well as the usefulness of using lifted Bell-like inequalities as device-independent witnesses for entanglement depth is also discussed.