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

TL;DR

This paper introduces the concept of witnesses for detecting causally nonseparable quantum processes, providing practical examples and methods to identify such processes beyond traditional causal order.

Contribution

It offers a simplified introduction to witnesses of causal nonseparability and demonstrates their construction and application through explicit case studies.

Findings

Witnesses can effectively detect causally nonseparable processes.

Explicit examples illustrate how to construct and use witnesses in practice.

The quantum switch exemplifies a causally nonseparable process.

Abstract

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.