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It is well-known that if one assumes quantum theory to hold locally, then processes with indefinite causal order and cyclic causal structures become feasible. Here, we study qualitative limitations on causal structures and correlations imposed by local quantum theory. For one, we find a necessary graph theoretic criterion--the "siblings-on-cycles" property--for a causal structure to be admissible: Only such causal structures admit a realization consistent with local quantum theory. We conjecture that this property is moreover sufficient. This conjecture is motivated by an explicit construction of quantum causal models, and supported by numerical calculations. We show that these causal models, in a restricted setting, are indeed consistent. For another, we identify two sets of causal structures that, in the classical-deterministic case, give rise to causal and non-causal correlations respectively., 8 pages, 3 figures

We show that the axiom of choice, a basic yet controversial postulate of set theory, leads to revise the standard understanding of one of the pillars of our best physical theories, namely the no-signaling principle. While it is well known that probabilistic no-signaling resources (such as quantum non-locality) are stronger than deterministic ones, we show-by invoking the axiom of choice-the opposite: Functional (deterministic) no-signaling resources can be stronger than probabilistic ones. To prove this, we devise a Bell-like game that shows a systematic advantage of functional no-signaling with respect to any probabilistic no-signaling resource., 5 pages, 3 figures

Quantum theory admits ensembles of quantum nonlocality without entanglement (QNLWE). These ensembles consist of seemingly classical states (they are perfectly distinguishable and non-entangled) that cannot be perfectly discriminated with local operations and classical communication (LOCC). Here, we analyze QNLWE from a causal perspective, and show how to perfectly discriminate some of these ensembles using local operations and classical communication without definite causal order. Specifically, three parties with access to an instance of indefinite causal order -- the AF/BW process -- can perfectly discriminate the states in a QNLWE ensemble -- the SHIFT ensemble -- with local operations. Hence, this type of quantum nonlocality disappears at the expense of definite causal order. Moreover, we show how multipartite generalizations of the AF/BW process are transformed into multiqubit ensembles that exhibit QNLWE. Such ensembles are of independent interest for cryptographic protocols and for the study of separable quantum operations unachievable with LOCC., Comment: 6 pages, 2 figures, comments welcome! v3: new title, improved presentation

Reichenbach's principle states that in a causal structure, correlations of classical information can stem from a common cause in the common past or a direct influence from one of the events in correlation to the other. The difficulty of explaining Bell correlations through a mechanism in that spirit can be read as questioning either the principle or even its basis: causality. In the former case, the principle can be replaced by its quantum version, accepting as a common cause an entangled state, leaving the phenomenon as mysterious as ever on the classical level (on which, after all, it occurs). If, more radically, the causal structure is questioned in principle, closed space-time curves may become possible that, as is argued in the present note, can give rise to non-local correlations if to-be-correlated pieces of classical information meet in the common future --- which they need to if the correlation is to be detected in the first place. The result is a view resembling Brassard and Raymond-Robichaud's parallel-lives variant of Hermann's and Everett's relative-state formalism, avoiding "multiple realities.", Comment: 8 pages, 5 figures

General relativity allows for the existence of closed time-like curves, along which a material object could travel back in time and interact with its past self. This possibility raises the question whether certain initial conditions, or more generally local operations, lead to inconsistencies and should thus be forbidden. 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., Comment: 11 pages, 3 figures

The difficulty of explaining non-local correlations in a fixed causal structure sheds new light on the old debate on whether space and time are to be seen as fundamental. Refraining from assuming space-time as given a priori has a number of consequences. First, the usual definitions of randomness depend on a causal structure and turn meaningless. So motivated, we propose an intrinsic, physically motivated measure for the randomness of a string of bits: its length minus its normalized work value, a quantity we closely relate to its Kolmogorov complexity (the length of the shortest program making a universal Turing machine output this string). We test this alternative concept of randomness for the example of non-local correlations, and we end up with a reasoning that leads to similar conclusions as in, but is conceptually more direct than, the probabilistic view since only the outcomes of measurements that can actually all be carried out together are put into relation to each other. In the same context-free spirit, we connect the logical reversibility of an evolution to the second law of thermodynamics and the arrow of time. Refining this, we end up with a speculation on the emergence of a space-time structure on bit strings in terms of data-compressibility relations. Finally, we show that logical consistency, by which we replace the abandoned causality, it strictly weaker a constraint than the latter in the multi-party case., Comment: 17 pages, 16 figures, small corrections

Bell non-local correlations cannot be naturally explained in a fixed causal structure. This serves as a motivation for considering models where no global assumption is made beyond logical consistency. The assumption of a fixed causal order between a set of parties, together with free randomness, implies device-independent inequalities --- just as the assumption of locality does. It is known that local validity of quantum theory is consistent with violating such inequalities. Moreover, for three parties or more, even the (stronger) assumption of local classical probability theory plus logical consistency allows for violating causal inequalities. Here, we show that a classical environment (with which the parties interact), possibly containing loops, is logically consistent if and only if whatever the involved parties do, there is exactly one fixed-point, the latter being representable as a mixture of deterministic fixed-points. We further show that the non-causal view allows for a model of computation strictly more powerful than computation in a world of fixed causal orders., Comment: 24 pages, 8 figures, 4 tables

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., Comment: 14 pages, 12 figures, 1 table, improved, references updated