Characterizing Bell nonlocality and EPR steerability with quantum magic squares.

By exploiting the high-dimensional probability tensor, Li and Qiao (Quantum Inf Process 20:109, 2021) proposed quantum magic square (QMS) models to characterize the diverse forms of nonlocal phenomena and derived a conditional majorization uncertainty relation to witness quantum steering. Motivated by this work, we propose the concepts of the probability and operator QMSs (P-QMSs and O-QMSs) to characterize Bell nonlocality of a bipartite correlation tensor (BCT) and EPR steerability of a bipartite state. We prove that a BCT is Bell local if and only if it has a P-QMS for Alice or a P-QMS for Bob and a bipartite state shared by Alice and Bob is one-way unsteerable with a measurement assemblage of Alice if and only if it has an O-QMS. [ABSTRACT FROM AUTHOR]