Continuous-variable supraquantum nonlocality

TL;DR

This paper explores supraquantum nonlocal correlations in infinite-dimensional continuous-variable systems, introducing a formalism for no-signaling measures, demonstrating Gaussian supraquantum correlations, and characterizing the geometry of the no-signaling set.

Contribution

It develops a formalism for continuous-variable no-signaling correlations, introduces Gaussian supraquantum correlations, and characterizes the structure of the no-signaling set in this context.

Findings

Existence of supraquantum Gaussian correlations violating Tsirelson bound.

Introduction of continuous-variable Popescu-Rohrlich (PR) boxes as a limit case.

The convex hull of CV PR boxes is dense and they are extreme points in the no-signaling set.

Abstract

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.