Non-signalling conditions encode minimal requirements that any (quantum) systems must satisfy in order to be consistent with special relativity. Recent works have argued that in scenarios involving more than two parties, correlations compatible with relativistic causality do not have to satisfy all possible non-signalling conditions but only a subset of them. Here we show that correlations satisfying only this subset of constraints have to satisfy highly non-local monogamy relations between the effects of space-like separated random variables. These monogamy relations take the form of entropic inequalities between the various systems and we give a general method to derive them. Using these monogamy relations, we refute previous suggestions for physical mechanisms that could lead to relativistically causal correlations, demonstrating that such mechanisms would lead to superluminal signalling.
Non-signalling conditions encode minimal requirements that any (quantum) systems must satisfy in order to be consistent with special relativity. Recent works have argued that in scenarios involving more than two parties, correlations compatible with relativistic causality do not have to satisfy all possible non-signalling conditions but only a subset of them. Here we show that correlations satisfying only this subset of constraints have to satisfy highly non-local monogamy relations between the effects of space-like separated random variables. These monogamy relations take the form of entropic inequalities between the various systems and we give a general method to derive them. Using these monogamy relations, we refute previous suggestions for physical mechanisms that could lead to relativistically causal correlations, demonstrating that such mechanisms would lead to superluminal signalling.
The no-signaling constraints state that the probability distribution of the outputs of any subset of parties is independent of the inputs of the complementary set; here we re-examine these to see how they arise from relativistic causality. We show that while the usual no-signaling constraints are sufficient, in general they are not necessary to ensure that a theory does not violate causality. Depending on the exact space-time coordinates of the measurement events in a multi-party Bell experiment, causality only imposes a subset of the usual no-signaling conditions. After revisiting the derivation of the two-party no-signaling constraints, we consider the three-party Bell scenario and characterise a space-time region in which a subset of the no-signaling conditions is sufficient to preserve causality. Secondly, we examine the implications for device-independent cryptography against an eavesdropper constrained only by the laws of relativity. We show an explicit attack in certain measurement configurations on a family of protocols based on the n-party Mermin inequalities that were previously proven secure under the old no-signaling conditions. We then show that security of two-party protocols can also be compromised when the eavesdropper's measurement configuration is not constrained. The monogamy of non-local correlations that underpin their use in secrecy can also be broken in certain space-time configurations. Thirdly, we inspect the notion of free-choice and propose a definition of free-choice in the multi-party Bell experiment. We then re-examine the question whether quantum correlations may admit explanations by finite speed superluminal influences. Finally, we study genuine multiparty non-locality and present a new class of causal bilocal models. We propose a new Svetlichny-type inequality that is satisfied by the causal bilocal model and show its violation within quantum theory.
The characterization of non-local correlations with respect to the causal order of events in spacetime is still an open question. We systematically investigate the polytope of relativistic causal boxes in the three-party Bell scenario and compute the complete set of extremal boxes in the (3,2,2) scenario with three parties each performing two binary measurements. We highlight the difference with the usual no-signaling polytope by computing the dimension of the RC polytope and contrasting the RC bounds for some well-known multi-player games. We show that no two-party Bell inequality obeys a monogamy relation when constrained only by causality as opposed to the no-signaling conditions. We identify multi-party Bell inequalities and measurement configurations where trade-off relations do exist, showing that device-independent cryptography against adversaries constrained only by relativistic causality is still not excluded.
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 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.
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.
The ubiquitous no-signaling constraints state that the probability distributions of outputs of any subset of parties in a Bell experiment are independent of remaining parties' inputs. These constraints are considered to form ultimate limits for physical correlations and led to the fields of post-quantum cryptography, randomness generation besides identifying information-theoretic principles underlying quantum theory. Here we show that while these constraints are sufficient, they are not necessary to enforce relativistic causality in multi-party correlations, i.e., the rule that correlations do not allow casual loops. Depending on the space-time coordinates of the measurement events, causality only imposes a subset of no-signaling conditions. We first consider the n-party Bell experiment (n > 2) and identify all configurations where subsets of the constraints suffice. Secondly, we examine the implications for device-independent cryptography against an eavesdropper constrained only by relativity, detailing among other effects explicit attacks on well-known randomness amplification and key distribution protocols.