Uncertainty principle as a postquantum nonlocality witness for the continuous-variable multimode scenario

The uncertainty principle is one of the central concepts in quantum theory. Different forms of this principle have been discussed in various foundational and information theoretic topics. Whereas in the discrete input-output scenario the limited nonlocal behavior of quantum theory has been explained by the fine-grained uncertainty relation, in the continuous-variable paradigm the Robertson-Schrodinger (RS) uncertainty relation has been used to detect multimode entanglement. Here we show that the RS uncertainty relation plays an important role in discriminating between quantum and postquantum nonlocal correlations in the multimode continuous outcome scenario. We provide a class of m-mode postquantum nonlocal correlations with a continuous outcome spectrum. While nonlocality of the introduced class of correlations is established through the Calvalcanti-Foster-Reid-Drummond class of Bell inequalities, the RS uncertainty relation detects their postquantum nature. Our result suggests a wider role of the uncertainty principle in the study of nonlocality in continuous-variable multimode systems.