On the definition and characterisation of multipartite causal (non)separability

TL;DR

This paper compares different definitions of multipartite causal nonseparability, proposes a new natural definition, and develops practical criteria and witnesses for identifying causally nonseparable processes.

Contribution

It introduces a unified, natural definition of multipartite causal nonseparability and provides practical tests and witnesses for its detection.

Findings

Demonstrates inequivalence of existing tripartite and multipartite definitions.

Proposes a new, natural definition of causal nonseparability.

Derives necessary and sufficient conditions for practical detection.

Abstract

The concept of causal nonseparability has been recently introduced, in opposition to that of causal separability, to qualify physical processes that locally abide by the laws of quantum theory, but cannot be embedded in a well-defined global causal structure. While the definition is unambiguous in the bipartite case, its generalisation to the multipartite case is not so straightforward. Two seemingly different generalisations have been proposed, one for a restricted tripartite scenario and one for the general multipartite case. Here we compare the two, showing that they are in fact inequivalent. We propose our own definition of causal (non)separability for the general case, which---although a priori subtly different---turns out to be equivalent to the concept of "extensible causal (non)separability" introduced before, and which we argue is a more natural definition for general multipartite scenarios. We then derive necessary, as well as sufficient conditions to characterise causally (non)separable processes in practice. These allow one to devise practical tests, by generalising the tool of witnesses of causal nonseparability.