Simulating all multipartite non-signalling channels via quasiprobabilistic mixtures of local channels in generalised probabilistic theories

TL;DR

This paper demonstrates that all multipartite non-signalling channels in generalised probabilistic theories can be simulated by affine combinations of local channels, extending previous bipartite results to a broader theoretical framework.

Contribution

It generalizes the simulation of non-signalling channels to multipartite scenarios within generalised probabilistic theories, including quantum theory, using Hardy's duotensor formalism.

Findings

Non-signalling channels can be simulated by affine combinations of local operations.

The results apply to quantum theory and other generalised probabilistic theories.

The proof leverages Hardy's duotensor formalism for the simulation.

Abstract

Non-signalling quantum channels -- relevant in, e.g., the study of Bell and Einstein-Podolsky-Rosen scenarios -- may be simulated via affine combinations of local operations in bipartite scenarios. Moreover, when these channels correspond to stochastic maps between classical variables, such simulation is possible even in multipartite scenarios. These two results have proven useful when studying the properties of these channels, such as their communication and information processing power, and even when defining measures of the non-classicality of physical phenomena (such as Bell non-classicality and steering). In this paper we show that such useful quasi-stochastic characterizations of channels may be unified and applied to the broader class of multipartite non-signalling channels. Moreover, we show that this holds for non-signalling channels in quantum theory, as well as in a larger family of generalised probabilistic theories. More precisely, we prove that non-signalling channels can always be simulated by affine combinations of corresponding local operations, provided that the underlying physical theory is locally tomographic -- a property that quantum theory satisfies. Our results then can be viewed as a generalisation of Refs.~[Phys. Rev. Lett. 111, 170403] and [Phys. Rev. A 88, 022318 (2013)] to the multipartite scenario for arbitrary tomographically local generalised probabilistic theories (including quantum theory). Our proof technique leverages Hardy's duotensor formalism, highlighting its utility in this line of research.