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Causal inequalities are bounds on correlations obtained when operations take place in a causal sequence, i.e. in which the background time or definite causal structure pre-exists such that every operation is either in the future, in the…

Quantum mechanics allows for coherent control over the order in which different processes take place on a target system, giving rise to a new feature known as indefinite causal order. Indefinite causal order provides a resource for quantum…

The idea that events obey a definite causal order is deeply rooted in our understanding of the world and at the basis of the very notion of time. But where does causal order come from, and is it a necessary property of nature? We address…

Quantum theory is in principle compatible with processes that violate causal inequalities, an analogue of Bell inequalities that constrain the correlations observed by sets of parties operating in a definite causal order. Since the…

It has been shown that it is theoretically possible for there to exist quantum and classical processes in which the operations performed by separate parties do not occur in a well-defined causal order. A central question is whether and how…

The study of causal relations has recently been applied to the quantum realm, leading to the discovery that not all physical processes have a definite causal structure. While indefinite causal processes have previously been experimentally…

Recent developments in the formalisation of quantum causal structures have made it possible to test and compare hypotheses about causal structure empirically, rather than being a-priori assumptions. Such differences in causal structure may…

It has long been recognized that certain quantum correlations are incompatible with particular assumption about classical causal structure. Given a causal structure of unknown classicality, the presence of such correlations certifies the…

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)…

In a scenario where two parties share, act on and exchange some physical resource, the assumption that the parties' actions are ordered according to a definite causal structure yields constraints on the possible correlations that can be…

Causal reasoning is essential to science, yet quantum theory challenges it. Quantum correlations violating Bell inequalities defy satisfactory causal explanations within the framework of classical causal models. What is more, a theory…

Classically the causal order of two timelike separated events A and B is fixed -- either A before B or B before A. This is no longer true in quantum theory, where it is possible to encounter superpositions of causal orders. The quantum…

Within quantum theory, we can create superpositions of different causal orders of events, and observe interference between them. This raises the question of whether quantum theory can produce results that would be impossible to replicate…

Quantum inequalities are bounds on negative time-averages of the energy density of a quantum field. They can be used to rule out exotic spacetimes in general relativity. We study quantum inequalities for a scalar field with a background…

It is shown that in the 4d Euclidean space there are two causal structures defined by the temporal field. One of them is well-known Minkowski spacetime. In this case the gravitational potential (the positive definite Riemann metric) and…

In general relativity, `causal structure' refers to the partial order on space-time points (or regions) that encodes time-like relationships. Recently, quantum information and quantum foundations saw the emergence of a `causality…

Processes with indefinite causal order can arise when quantum theory is locally valid and they allow accomplishing new informational tasks. Despite recent progress, the correlations allowed in such processes have not been clearly…

Time-reversal symmetry is a prevalent feature of microscopic physics, including operational quantum theory and classical general relativity. Previous works have studied indefinite causal structure using the language of operational quantum…

Recent results on causality in noncommutative space-time are reviewed. We study, in particular, quantum causal structures in 1+1 dimensional kappa Minkowski space-time. This later is described by a twisted Lorentzian Spectral Triple build…

Investigating the role of causal order in quantum mechanics has recently revealed that the causal distribution of events may not be a-priori well-defined in quantum theory. While this has triggered a growing interest on the theoretical…