Quantum theory in a global space-time gives rise to non-local correlations, which cannot be explained causally in a satisfactory way; this motivates the study of theories with reduced global assumptions. Oreshkov, Costa, and Brukner (2012) proposed a framework in which quantum theory is valid locally but where, at the same time, no global space-time, i.e., predefined causal order, is assumed beyond the absence of logical paradoxes. It was shown for the two-party case, however, that a global causal order always emerges in the classical limit. Quite naturally, it has been conjectured that the same also holds in the multi-party setting. We show that counter to this belief, classical correlations locally compatible with classical probability theory exist that allow for deterministic signaling between three or more parties incompatible with any predefined causal order.
Classical correlations without predefined causal order arise from processes where parties manipulate random variables, and where the order of these interactions is not predefined. No assumption on the causal order of the parties is made, but the processes are restricted to be logically consistent under any choice of the parties' operations. It is known that for three parties or more, this set of processes is larger than the set of processes achievable in a predefined ordering of the parties. Here, we model all classical processes without predefined causal order geometrically and find that the set of such processes forms a polytope. Additionally, we model a smaller polytope-the deterministic-extrema polytope-where all extremal points represent deterministic processes. This polytope excludes probabilistic processes that must be-quite unnaturally-fine-tuned, because any variation of the weights in a decomposition into deterministic processes leads to a logical inconsistency. Motivation and main resultAn assumption often made in physical theories, sometimes implicitly, is the existence of a global time. In particular, quantum theory is formulated with time as an intrinsic parameter. If one relaxes this assumption by requiring local validity of some theory and logical consistency only, then a larger set of correlations can be obtained, called correlations without predefined causal order. The processes that lead to such correlations are called processes without predefined causal order. Two motivations to study such correlations are quantum gravity and quantum non-locality. Quantum gravity motivates this research in the sense that on the one hand, relativity is a deterministic theory equipped with a dynamic spacetime; on the other hand, quantum theory is a probabilistic theory embedded in a fixed spacetime. This suggests that quantum gravity is relaxed in both aspects, i.e.,it is a probabilistic theory equipped with a dynamic spacetime [1]. Quantum non-local correlations [2][3][4] motivate this study since the possibility of a satisfactory causal explanation [5] for such correlations is questionable [3,[6][7][8][9][10][11][12][13]. Dropping the notion of a global time or of an a priori spacetime-as has been suggested from different fields of research[14-23]-dissolves this paradox. This can be achieved by defining causal relations based on free randomness (see figure 1) as opposed to defining free randomness based on causal relations [24,25]. Such an approach gives a dynamic character to causality; causal connections are not predefined but are derived from the observed correlations.Relaxations of quantum theory where the assumption of a global time is dropped have recently been studied widely [1, 26-45] (see [46] for a review). Our work follows the spirit of an operational quantum framework for such correlations developed by Oreshkov et al [31]. Some correlations appearing in their quantum framework -for two parties or more-cannot be simulated by assuming a predefined causal order of the parties. Such correlations ar...
General relativity predicts the existence of closed time-like curves, along which a material object could travel back in time and interact with its past self. The natural question is whether this possibility leads to inconsistencies: Could the object interact in such a way to prevent its own time travel? If this is the case, self-consistency should forbid certain initial conditions from ever happening, a possibility at odds with the local nature of dynamical laws. Here we consider the most general deterministic dynamics connecting classical degrees of freedom defined on a set of bounded space-time regions, requiring that it is compatible with arbitrary operations performed in the local regions. We find that any such dynamics can be realised through reversible interactions. We further find that consistency with local operations is compatible with non-trivial time travel: Three parties can interact in such a way to be all both in the future and in the past of each other, while being free to perform arbitrary local operations. We briefly discuss the quantum extension of the formalism.
The paradigmatic view where information is seen as a more fundamental concept than the laws of physics leads to a different understanding of spacetime where the causal order of events emerges from correlations between random variables representing physical quantities. In particular, such an information-theoretic approach does not enforce a global spacetime structure. By following this path, we conclude that perfect signaling correlations among three parties are possible which do not obey the restrictions imposed by global spacetime. We show this using a recent framework based on the sole assumptions that locally, quantum theory is valid and random variables can be described by probability distributions. Our result is of zero-error type and is an analog to a tripartite appearance of quantum non-locality which manifests itself by satisfying a condition with certainty whereas the same is impossible for any local theory.Comment: 5 pages, 3 figures, 2 tables, references adde
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