The operational no-signalling constraints and their implications

TL;DR

The paper develops a unified operational no-signalling framework to analyze both spacelike and timelike correlations in general relativistic spacetimes via spacetime random variables (SRVs). It proves that operational no-signalling constraints are necessary and sufficient to exclude operational superluminal loops and explores the possibility of jamming nonlocal correlations without requiring superluminal signalling, including in black hole spacetimes. The authors show Minkowski-space paradoxes or symmetry violations arise if the constraints fail, while curved spacetimes admit only local implications; they also critique prior claims about jamming and monogamy by deriving general constraints and showing that monogamies reflect constraint tensions rather than impossibility. The results have implications for device-independent cryptography and information processing in diverse spacetimes, and they outline a path for applying the framework to other spacetime models and protocols.

Abstract

The study of quantum correlations within relativistic spacetimes, and the consequences of relativistic causality on information processing using such correlations, has gained much attention in recent years. In this paper, we establish a unified framework in the form of operational no-signalling constraints to study both nonlocal and temporal correlations within general relativistic spacetimes. We explore several intriguing consequences arising from our framework. Firstly, we show that the violation of the operational no-signalling constraints in Minkowski spacetime implies either a logical paradox or an operational infringement of Poincaré symmetry. We thereby examine and subvert recent claims in [Phys. Rev. Lett. 129, 110401 (2022)] on the possibility of witnessing operationally detectable causal loops in Minkowski spacetime. Secondly, we explore the possibility of jamming of nonlocal correlations, controverting a recent claim in [Nat. Comm. 16, 269 (2025)] that a physical mechanism for jamming would necessarily lead to superluminal signalling. Finally, we show that in black hole spacetimes certain nonlocal correlations under and across the event horizon can be jammed by any agent without spoiling the operational no-signalling constraints.

Figures (8)

• Figure 1: An illustration of the operational separation relation. In panel a) all points $q_1,q_2,q_1',q_2'$ are operationally separated from the point $p$. Also, both tuples $(q_1,q_2)$ and $(q_1',q_2')$ are operationally separated from $p$, because there exist gathering points, $Q$ and $Q'$ respectively, which lie outside of $p$'s future. On the other hand, $p$ is operationally separated from $(q_1,q_2)$, but it is not operationally separated from $(q_1',q_2')$. In panel b) the tuple $(q_1,q_2)$ is not operationally separated from $p$, although both single points $q_1$ and $q_2$ are operationally separated from $p$. Also, $p$ is operationally separated from $q_1$, and $q_2$, and $(q_1,q_2)$.
• Figure 2: An illustration of the signalling protocol exploiting a violation of constraint \ref{['ONS_new']}. See text for the description.
• Figure 3: Conformal diagrams for the Minkowski, a), and Schwarzschild, b), spacetimes (see e.g. ChruscielBH). a) In Minkowski spacetime any tuple of points have a non-empty common future, and hence a gathering point. b) The tuple $(q_1,q_2)$ has a gathering point, but this is not the case for the tuples $(q_1,q_3)$, $(q_2,q_3)$ and $(q_1,q_2,q_3)$.
• Figure 4: A spacetime diagram illustrating an operational causal loop exploiting a violation of no-signalling constraints \ref{['ONS_new']} and the special principle of relativity \ref{['Poincare']}. The arrows represent causal influences between SRVs, subluminal (green) and superluminal (red). See text for further description.
• Figure 5: A consistent embedding of the causal model $\mathcal{G}^\text{loop}$ from Loops_PRL in Minkowski spacetime. See text for the description.

Theorems & Definitions (11)

• Definition 1
• Definition 2
• Theorem 3
• Theorem 4
• Corollary 5
• Proposition 6
• Definition 7
• Corollary 8
• Definition 9
• Theorem 10