Characterizing quantum nonlocalities per uncertainty relation

Nonlocality is one of the distinctive features of quantum mechanics and has different forms in practice, e.g., non-separability, quantum steering, and Bell nonlocality. Here, by exploiting the high-dimensional probability tensor, we propose a quantum magic square model to characterize the diverse forms of nonlocal phenomena in a single protocol. In this model, the nonlocalities are manifested in the partial-sums of the probability tensor, where the uncertainty relation serves as an indicator of different nonlocal phenomena. We derive a conditional majorization uncertainty relation criterion to witness the quantum steering. The new criterion is applicable to infinite number of observables and is found superior to the formerly thought optimal steering criterion.

Automated summary

This study introduces a quantum magic square model using high-dimensional probability tensor to characterize different forms of nonlocal phenomena; nonlocalities are shown in the partial-sums of the probability tensor, with uncertainty relation serving as an indicator. They also develop a new quantum steering detection criterion, applicable to an infinite number of observables.