  Supraquantum nonlocality refers to correlations that are more nonlocal than
allowed by quantum theory but still physically conceivable in post-quantum
theories, in the sense of respecting the basic no-faster-than-light
communication principle. While supraquantum correlations are relatively well
understood for finite-dimensional systems, little is known in the
infinite-dimensional case. Here, we study supraquantum nonlocality for
bipartite systems with two measurement settings and infinitely many outcomes
per subsystem. We develop a formalism for generic no-signaling black-box
measurement devices with continuous outputs in terms of probability measures,
instead of probability distributions, which involves a few technical
subtleties. We show the existence of a class of supraquantum Gaussian
correlations, which violate the Tsirelson bound of an adequate
continuous-variable Bell inequality. We then introduce the continuous-variable
version of the celebrated Popescu-Rohrlich (PR) boxes, as a limiting case of
the above-mentioned Gaussian ones. Finally, we perform a characterisation of
the geometry of the set of continuous-variable no-signaling correlations.
Namely, we show that that the convex hull of the continuous-variable PR boxes
is dense in the no-signaling set. We also show that these boxes are extreme in
the set of no-signaling behaviours and provide evidence suggesting that they
are indeed the only extreme points of the no-signaling set. Our results lay the
grounds for studying generalized-probability theories in continuous-variable
systems.
