On the edge of the set of no-signaling assemblages

TL;DR

This paper introduces the concept of the edge of no-signaling assemblages in multipartite steering, characterizes it, and explores its implications for quantum realizability and the construction of witnesses for nonlocal assemblages.

Contribution

It defines and characterizes the edge of no-signaling assemblages and develops witnesses for assemblages lacking local hidden state models, advancing understanding of multipartite quantum steering.

Findings

Characterization of the edge of no-signaling assemblages

Construction of witnesses for assemblages without LHS models

No-go result for assemblages on the edge with certain measurements

Abstract

Following recent advancements, we consider a scenario of multipartite postquantum steering and general no-signaling assemblages. We introduce the notion of the edge of the set of no-signaling assemblages and we present its characterization. Next, we use this concept to construct witnesses for no-signaling assemblages without an LHS model. Finally, in the simplest nontrivial case of steering with two untrusted subsystems, we discuss the possibility of quantum realization of assemblages on the edge. In particular, for three-qubit states, we obtain a no-go type result, which states that it is impossible to produce assemblage on the edge using measurements described by POVMs as long as the rank of a given state is greater than or equal to 3.