Composable simultaneous purification: when all communication scenarios reduce to spatial correlations

TL;DR

This paper extends the concept of simultaneous purification from bipartite to multipartite quantum communication scenarios, showing that all non-signalling correlations can be reduced to spatial quantum Bell correlations, with implications for understanding quantum resources.

Contribution

It unifies and extends simultaneous purification results to multipartite instruments and super-instruments, demonstrating that complex compositions cannot escape standard quantum Bell correlations.

Findings

All compositions of non-signalling assemblages are within spatial quantum Bell correlations.

Any non-signalling correlation outside this set requires at least one signalling assemblage.

The results apply to multipartite communication schemes, broadening previous bipartite findings.

Abstract

Bell non-locality is a powerful framework to distinguish classical, quantum and post-quantum resources, which relies on non-communicating players. Under which restriction can we have the same separations, if we allow for communication? Non-signalling state assemblages, and the fact that they can always be simultaneously purified, turned out to be the key element to restrict the simplest bipartite communication scenario, the prepare-and-measure, to the standard bipartite Bell scenario. Yet, many distinctive features of quantum theory are genuinely multipartite and cannot be reduced to two-party behaviour. In this work we are interested in extending this simultaneous purification inspired result to all multipartite communication schemes. As a first step, we unify and extend the simultaneous purification result from states to instruments and super-instruments, which are composable structures, and open up the possibility to explore more complex communication scenarios. Our main contribution is to establish that arbitrary compositions of non-signalling assemblages cannot escape the standard spatial quantum Bell correlations set. As a consequence, any interactive quantum realization of correlations outside of this set must involve at least one signalling assemblage of quantum operations, even when the resulting correlations are non-signalling.