Postquantum Steering

The discovery of postquantum nonlocality, i.e., the existence of nonlocal correlations that are stronger than any quantum correlations but nevertheless consistent with the no-signaling principle, has deepened our understanding of the foundations of quantum theory. In this work, we investigate whether the phenomenon of Einstein-Podolsky-Rosen steering, a different form of quantum nonlocality, can also be generalized beyond quantum theory. While post-quantum steering does not exist in the bipartite case, we prove its existence in the case of three observers. Importantly, we show that postquantum steering is a genuinely new phenomenon, fundamentally different from postquantum nonlocality. Our results provide new insight into the nonlocal correlations of multipartite quantum systems.

Figure 1

Bloch sphere representation of the postquantum assemblage ${\sigma }_{bc|yz}^{*}$. For each pair of settings $y,z$ we represent the four conditional real qubit states ${\sigma }_{bc|yz}^{*}$ in an equator of the Bloch sphere. The normalized state is given by its Bloch vector, while the normalization is indicated by the corresponding circle; more precisely, the distance to the origin corresponds to $p(bc|yz)=\mathrm{tr}({\sigma }_{bc|yz}^{*})$. The upper figure indicates the marginal states ${\sigma }_{b|y}^B$, as well as the reduced state ${\rho }_A^{*}$.