Witnesses of causal nonseparability: an introduction and a few case studies

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 [Ara\'ujo 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.Comment: 15 pages, 7 figure

The effectiveness of paired study versus individual study in social studies

Thesis (Ed.M.)--Boston Universit

Parallel application of a novel domain decomposition preconditioner for the adaptive finite-element solution of three-dimensional convection-dominated PDEs

We describe and analyse the parallel implementation of a novel domain decomposition preconditioner for the fast iterative solution of linear systems of algebraic equations arising from the discretization of elliptic partial differential equations (PDEs) in three dimensions. In previous theoretical work, this preconditioner has been proved to be optimal for symmetric positive-definite (SPD) linear systems. In this paper, we provide details of our three-dimensional parallel implementation and demonstrate that the technique may be generalized to the solution of non-symmetric algebraic systems, such as those arising when convection-diffusion problems are discretized using either Galerkin or stabilized finite-element methods (FEMs). Furthermore, we illustrate the potential of the preconditioner for use within an adaptive finite-element framework by successfully solving convection-dominated problems on locally, rather than globally, refined meshes

Communication through quantum-controlled noise

In a recent series of works [Ebler et al. Phys. Rev. Lett. 120, 120502 (2018); arXiv:1809.06655v2; arXiv:1810.10457v2], it has been proposed that the quantum superposition of causal order -- the quantum switch -- may offer an enhancement of classical and quantum channel capacity through noisy channels, a phenomena that was coined `causal activation'. In this paper we attempt to clarify the nature of the purported advantage, by comparing the quantum switch to a class of processes that can be interpreted as quantum superposition of processes with the same causal order. We show that some of these processes can match or even outperform the quantum switch at enhancing classical and quantum channel capacity, and argue that they require the same resources as the switch. We conclude, in agreement with Abbott et al. [arXiv:1810.09826v1], that the aforementioned advantages appear to be attributable to the ability to coherently control quantum operations, and not to indefinite causal order per se.Comment: 8 pages, 1 figure. Published versio