Multipartite channel assemblages

TL;DR

This paper extends the concept of channel steering to multipartite scenarios, characterizes the differences between no-signaling and quantum assemblages, and explores secure key distribution under relaxed no-signaling conditions.

Contribution

It introduces multipartite no-signaling channel assemblages, provides a complete characterization using Choi-Jamiołkowski isomorphism, and analyzes secure key certification in relaxed no-signaling scenarios.

Findings

No-signaling and quantum descriptions differ beyond bipartite cases.

Complete characterization of assemblages via Choi-Jamiołkowski isomorphism.

Possibility of certifying secure key bits under relaxed no-signaling constraints.

Abstract

Motivated by the recent studies on post-quantum steering, we generalize the notion of bipartite channel steering by introducing the concept of multipartite no-signaling channel assemblages. We first show that beyond the bipartite case, the no-signaling and quantum descriptions of channel assemblages do not coincide. Using the Choi-Jamio{\l}kowski isomorphism, we present a complete characterization of these classes of assemblages and use this characterization to provide sufficient conditions for extremality of quantum channel assemblages within the set of all no-signaling channel assemblages. Finally, we introduce and discuss a relaxed version of channel steering where only certain subsystems obey the no-signaling constraints. In this latter asymmetric scenario we show the possibility of certifying a perfect key bit that is secure against a general no-signaling eavesdropper.