Every non-signalling channel is common-cause realizable

TL;DR

This paper proves that in certain probabilistic theories like quantum mechanics, all non-signalling channels can be realized through common causes within the same theory, unifying resource and causal perspectives.

Contribution

It demonstrates that non-signalling resources are exactly those realizable by GPT-based common causes, resolving an open question and linking resource theories with causal structures.

Findings

Non-signalling channels are GPT-common-cause realizable.

All non-signalling assemblages can be realized in a GPT.

Provides a causal interpretation for non-signalling resources.

Abstract

In this work we show that the set of non-signalling resources of a locally-tomographic generalised probabilistic theory (GPT), such as quantum and classical theory, coincides with its set of GPT-common-cause realizable resources, where the common causes come from an associated GPT. From a causal perspective, this result provides a reason for, in the study of resource theories of common-cause processes, taking the non-signalling channels as the resources of the enveloping theory. This answers a critical open question in Ref.~\cite{schmid2020postquantum}. An immediate corollary of our result is that every non-signalling assemblage is realizable in a GPT, answering in the affirmative the question posed in Ref.~\cite{cavalcanti2022post}.