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arXiv:2311.18465

The standard no-signalling constraints in Bell scenarios are neither sufficient nor necessary for preventing superluminal signalling with general interventions

V. Vilasini, Roger Colbeck

Published Nov 30, 2023• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2311.18465

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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.
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.
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.
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.
The no-signalling principle lies at the heart of Bell-type experiments involving spacelike-separated parties. Although not all no-signalling correlations can be realized within quantum theory, the no-sinalling principle itself remains fundamental even for post-quantum theories, since its violation would imply superluminal signalling. In the spirit of device independent nature of the Bell inequalities, there has recently been growing interest in causal inequalities, which identify correlations admitting no causal explanation. Such correlations have been rigorously studied within the process-matrix formalism, which is built upon a constraint analogous to spacelike separation in Bell scenarios. We refer to this constraint as the single-interaction constraint, whereby each party interacts with the environment only once. Despite considerable effort, no fundamental guiding principle is currently known that characterizes the restrictions this constraint imposes on the correlations generated by Process Matrices. In this work, we address this gap by proposing a generalized causality principle for the bipartite case. We show that for certain cases, the generalised causality principle defines a strict subset of the set of all signalling correlations. This principle thus provides a fundamental limit on quantum and even post-quantum theories subject to the single-interaction constraint. By analogy with no-signalling, whose violation excludes certain causal structures among the parties, a violation of the generalised causality principle rules out a corresponding class of causal structures(causal structures with the single interaction constraint). More broadly, our techniques provide a general framework for deriving generalised causal constraints, applicable to a wide class of indefinite-causal-order scenarios.
Relativistic causality in certain spacetime configurations permits jamming - superluminal causal influences that nevertheless do not enable superluminal signaling. We fully characterize the correlations compatible with relativistic causality (RC) by extending the operator framework of PRL 104, 140404. When the underlying state is required to be quantum, we prove that any nontrivial jamming - whether state-independent or state-dependent - necessarily leads to hidden superluminal signaling. Thus, the only consistent possibilities are standard quantum correlations without jamming or the full relativistically causal correlation set, with intermediate jamming extensions of quantum correlations leading to signaling. As an application of our characterization, we investigate the security of device-independent (DI) cryptographic primitives against adversaries constrained only by relativistic causality. We construct explicit RC attacks that break DI bit commitment and DI secret sharing in jamming geometries, even when these protocols remain secure against no-signaling adversaries. Our results show that security against relativistic adversaries requires behaviors to be specified together with the spacetime locations of their measurement events; input-output statistics alone are insufficient.
Causal modeling is a tool for generating causal explanations of observed correlations and has led to a deeper understanding of correlations in quantum networks. Existing frameworks for quantum causality tend to focus on acyclic causal structures that are not fine-tuned i.e., where causal connections between variables necessarily create correlations between them. However, fine-tuned causal models (which permit causation without correlation) play a crucial role in cryptography, and cyclic causal models can be used to model physical processes involving feedback and may also be relevant in exotic solutions of general relativity. Here we develop a causal modeling framework capable of dealing with these general scenarios. The key feature of our framework is that it allows operational and relativistic notions of causality to be independently defined and for connections between them to be established in a theory-independent manner. The framework first gives an operational way to study causation that allows for cyclic, fine-tuned, and nonclassical causal influences. We then consider how a causal model can be embedded in a space-time structure (modeled as a partial order) and propose a compatibility condition for ensuring that the embedded causal model does not allow signaling outside the space-time future. We identify several distinct classes of causal loops that can arise in our framework, showing that compatibility with a space-time can rule out only some of them. We discuss conditions for preventing superluminal signaling within arbitrary (and possibly cyclic) causal structures and consider models of causation in postquantum theories admitting so-called jamming correlations. Finally, this work introduces the concept of a higher-order affects relation, which is useful for causal discovery in fined-tuned causal models.