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It was recently realised that quantum theory allows for so-called causally nonseparable processes, which are incompatible with any definite causal order. This was first suggested on a rather abstract level by the formalism of process matrices, which only assumes that quantum theory holds locally in some observers laboratories, but does not impose a global causal structure; it was then shown, on a more practical level, that the quantum switch---a new resource for quantum computation that goes beyond causally ordered circuits---provided precisely a physical example of a causally nonseparable process. To demonstrate that a given process is causally nonseparable, we introduced in [Araujo et al., New J. Phys. 17, 102001 (2015)] the concept of witnesses of causal nonseparability. Here we present a shorter introduction to this concept, and concentrate on some explicit examples to show how to construct and use such witnesses in practice.
Our common understanding of the physical world deeply relies on the notion that events are ordered with respect to some time parameter, with past events serving as causes for future ones. Nonetheless, it was recently found that it is possible to form
While the standard formulation of quantum theory assumes a fixed background causal structure, one can relax this assumption within the so-called process matrix framework. Remarkably, some processes, termed causally nonseparable, are incompatible with
A standard assumption for causal inference from observational data is that one has measured a sufficiently rich set of covariates to ensure that within covariate strata, subjects are exchangeable across observed treatment values. Skepticism about the
A symmetry witness is a suitable subset of the space of selfadjoint trace class operators that allows one to determine whether a linear map is a symmetry transformation, in the sense of Wigner. More precisely, such a set is invariant with respect to
Quantum entanglement lies at the heart of quantum mechanical and quantum information processing. Following the question who emph{witnesses} entanglement witnesses, we show entangled states play as the role of super entanglement witnesses. We show sep