The no-signaling principle preventing superluminal communication is a limiting paradigm for physical theories. Within the information-theoretic framework it is commonly understood in terms of admissible correlations in composite systems. Here we unveil its complementary incarnation---the ''dynamical no-signaling principle''---which forbids superluminal signaling via measurements on simple physical objects (e.g., particles) evolving in time. We show that it imposes strong constraints on admissible models of dynamics. The posited principle is universal; it can be applied to any theory (classical, quantum, or postquantum) with well-defined rules for calculating detection statistics in spacetime. As an immediate application we show how one could exploit the Schr\"odinger equation to establish a fully operational superluminal protocol in the Minkowski spacetime. This example illustrates how the principle can be used to identify the limits of applicability of a given model of quantum or postquantum dynamics.
The no-signaling principle preventing superluminal communication is a limiting paradigm for physical theories. Within the information-theoretic framework it is commonly understood in terms of admissible correlations in composite systems. Here we unveil its complementary incarnation---the ''dynamical no-signaling principle''---which forbids superluminal signaling via measurements on simple physical objects (e.g., particles) evolving in time. We show that it imposes strong constraints on admissible models of dynamics. The posited principle is universal; it can be applied to any theory (classical, quantum, or postquantum) with well-defined rules for calculating detection statistics in spacetime. As an immediate application we show how one could exploit the Schr"odinger equation to establish a fully operational superluminal protocol in the Minkowski spacetime. This example illustrates how the principle can be used to identify the limits of applicability of a given model of quantum or postquantum dynamics.
Causality is fundamental to science, but it appears in several different forms. One is relativistic causality, which is tied to a spacetime structure and forbids signaling outside the future. A second is an operational notion of causation that considers the flow of information between physical systems and interventions on them. In [V. Vilasini and R. Colbeck, General framework for cyclic and fine-tuned causal models and their compatibility with space-time, Phys. Rev. A 106, 032204 (2022).PLRAAN2469-992610.1103/PhysRevA.106.032204], we propose a framework for characterizing when a causal model can coexist with relativistic principles such as no superluminal signaling, while allowing for cyclic and nonclassical causal influences and the possibility of causation without signaling. In a theory without superluminal causation, both superluminal signaling and causal loops are not possible in Minkowski spacetime. Here we demonstrate that if we only forbid superluminal signaling, superluminal causation remains possible and show the mathematical possibility of causal loops that can be embedded in a Minkowski spacetime without leading to superluminal signaling. The existence of such loops in the given spacetime could in principle be operationally verified using interventions. This establishes that the physical principle of no superluminal signaling is not by itself sufficient to rule out causal loops between Minkowski spacetime events. Interestingly, the conditions required to rule out causal loops in a spacetime depend on the dimension. Whether such loops are possible in three spatial dimensions remains an important open question.
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 signaling (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 nonclassical correlations. We find a spacetime configuration in which this task cannot be achieved in any theory (classical, quantum, or postquantum) 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)-dimensional Minkowski spacetime, the task remains achievable in a configuration where measurement outcomes occur arbitrarily earlier in time than the settings, allowing a form of certifiable retrocausality without violating NSS. We illustrate our results by linking two different types of nonclassical postquantum 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 characterizing the information-theoretic structure of theories obeying such principles.
In PRL 129, 110401 it was shown that it is theoretically possible to have operationally detectable causal loops without violating the principle of no superluminal signalling (NSS) in (1+1)-Minkowski spacetime. Whether or not such causal loops are also possible in d>1 spatial dimensions, has remained a key open question. We resolve this question by showing that in a wide class of "conical" spacetimes, including Minkowski with d > 1, NSS does rule out all operationally detectable causal loops, in classical, quantum and post-quantum theories. This establishes that the relationship between the relativistic principles of NSS and no causal loops depends inherently on the geometry of spacetime.
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.
Non-classical correlations resulting from entangled quantum systems have sparked debates about the compatibility of quantum theory and relativity, and about the right way to think about causation. Key to a causal theory is that superluminal signalling is forbidden, which holds in quantum theory. In Bell scenarios, relativistic causality principles like no superluminal signalling are often assumed to follow from the standard no-signalling constraints on correlations. We explore the connections between a range of relativistic principles, including no superluminal signalling and no causal loops, and constraints on correlations that can arise with arbitrary interventions, within multi-party Bell scenarios. This includes standard no-signalling conditions and proposed relaxations allowing phenomena like jamming, where it was suggested that superluminal signalling and causal loops remain impossible. Using our recent framework combining relativistic principles with causal modelling, we show that any theory (classical or non-classical) allowing jamming must rely on causal fine-tuning and superluminal causal influences. Additionally, we show that jamming theories can lead to superluminal signalling in certain situations, highlighting limitations for their physicality. However, we identify cases where jamming correlations avoid superluminal signalling under general interventions, demonstrating that standard no-signalling constraints are not necessary for this purpose. We also show that these constraints are insufficient to rule out superluminal signalling and are neither necessary nor sufficient for ensuring no causal loops under general interventions. Finally, we derive necessary and sufficient conditions for ruling out superluminal signalling and operationally detectable causal loops, solidifying our understanding of relativistic causality principles in information processing tasks in space-time.
The Schrödinger-Newton equation aims at describing the dynamics of massive quantum systems subject to the gravitational self-interaction. As a deterministic nonlinear quantum wave equation, it is generally believed to conflict with the relativistic no-signalling principle. Here we challenge this viewpoint and show that it is of key importance to study the quantitative and operational character of the superluminal effects. To this end we employ a rigorous formalism of probability measures on spacetime and quantify the probability of a successful superluminal bit transfer via the single-particle Schrödinger-Newton equation. We demonstrate that such a quantity decreases with the increasing size and mass of the system. Furthermore, we prove that the Einstein-Dirac system, which yields the Schrödinger-Newton equation in the non-relativistic limit, is perfectly compatible with the relativistic causal structure. Our study demonstrates that the Schrödinger-Newton equation, which is by construction non-relativistic, is in fact `more compatible' with the no-signalling principle than the ordinary free Schrödinger equation.