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.
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.
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.
A fundamental question in device-independent quantum cryptography is to determine the minimal physical principle upon which the security of such a cryptographic protocol (such as for key distribution or for randomness generation) may be based. Since the seminal work on device-independent quantum key distribution by J. Barrett, L. Hardy, and A. Kent [Phys. Rev. Lett. 95, 010503 (2005)], a conjectured candidate for certification of device-independent security has been the principle of relativistic causality, namely the disallowance of causal loops. While this principle has thus far been equated with the no-signaling constraints, it has been shown recently that in multiparty Bell scenarios, the no-signaling constraints are sufficient but not necessary for relativistic causality, and a refined set of constraints has been proposed that more precisely capture the notion of relativistic causality. In this paper, we build upon this finding to show that, in contrast to the no-signaling constraints, the constraints of relativistic causality are not sufficient for certification of device-independent security. More specifically, we show that there exist correlations allowed by the causality principle that allow an adversary to gain complete information about the measurement outcomes of honest parties in any device-independent cryptographic protocol, thereby rendering the protocol completely insecure. As a tool to develop this adversarial attack strategy, we fully characterize the set of correlations allowed by relativistic causality in the tripartite Bell scenario of three parties, each performing two binary measurements, that may be of independent interest. We also demonstrate the difference between the relativistic causal correlations and those allowed by the usual no-signaling constraints by presenting explicit communication tasks wherein the two sets exhibit striking difference in their respective winning probabilities.
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.
Bell scenarios are multipartite scenarios that exclude any signalling between parties. This leads to a strict hierarchy of classical, quantum, and non-signalling correlations in such scenarios. Here we consider a minimal relaxation of non-signalling: each party is allowed to receive a system once, implement any local intervention on it, and send out the resulting system once. Crucially, unlike Bell, we make no global assumption about causal relations between parties, e.g., they could be embedded in some exotic spacetime with indefinite causal order. We do make a causal assumption local to each party, i.e., the input received by it causally precedes the output it sends out. We then ask: Can we device-independently certify the nonclassicality of multipartite correlations in such scenarios, just as Bell inequality violations do so in Bell scenarios? A priori, this is not clear: without some assumptions on the underlying physics (e.g., non-signalling), parties can realize arbitrary correlations. We therefore make a minimal assumption of logical consistency on the underlying physics, i.e., it must be free of time-travel antinomies without imposing any restrictions on local interventions of the parties. We then define antinomicity as a device-independent notion of nonclassicality and prove a strict hierarchy between correlation sets based on their antinomicity. An antinomic correlation cannot be explained by a classical physical theory compatible with free local interventions on pain of logical contradictions in the theory. On the other hand, parties exchanging quantum systems can witness antinomicity while respecting logical consistency. Antinomicity reduces to Bell nonlocality for non-signalling parties. It also resolves a conceptual puzzle, namely, the failure of causal inequalities as witnesses of nonclassicality: antinomicity implies causal inequality violations, but not conversely.
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.
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.