Theories with no superluminal signaling have greater information-processing power than theories with no superluminal causation

TL;DR

This paper explores how theories constrained by different relativistic causality principles, specifically no superluminal causation and no superluminal signalling, differ in their ability to generate non-classical correlations, revealing new insights into fundamental physics.

Contribution

It formalizes the distinction between NSC and NSS, demonstrating that violating NSC but satisfying NSS allows perfect achievement of certain non-classical tasks, unlike theories obeying NSC.

Findings

Theories violating NSC but satisfying NSS can achieve non-classical correlations.

A spacetime configuration where no theory obeying NSC can perform a specific task.

In (1+1)D Minkowski spacetime, retrocausality can be certifiably non-classical without NSS.

Abstract

A central goal in the foundations of physics is to understand the structure of physical theories, such as quantum theory, from physical principles. This is often explored by considering various information-theoretic principles. Here, we initiate a similar approach considering relativistic causality principles. No superluminal causation (NSC) and no superluminal signalling (NSS) are distinct relativistic principles, requiring, respectively, that causal influence/the ability of agents to signal are within the future lightcone. After formalizing their distinction, we investigate how well theories constrained by NSC and NSS perform in a task that involves generating non-classical correlations. We find a spacetime configuration in which this task cannot be achieved in any theory (classical, quantum, or post-quantum) satisfying NSC. However, we show that theories violating NSC but satisfying NSS can perfectly achieve the task. We give a protocol that would, in a world allowing superluminal causation, enable its operational certification without violating NSS, in general spacetimes. In the case of $(1+1)$D Minkowski spacetime, the task remains achievable in a configuration where measurement outcomes occur arbitrarily earlier in time than the settings, allowing a new form of certifiable retrocausality without violating NSS. We illustrate our results by linking two different types of non-classical post-quantum resources: PR-boxes and jamming. Our work offers insights into the role of different relativistic causality principles in fundamental physics and paves the way for characterising the information-theoretic structure of theories obeying such principles.