No-local-broadcasting theorem for non-signalling behaviours and assemblages

TL;DR

This paper proves a conjecture that nonlocal quantum behaviors cannot be locally broadcast, extending the no-broadcasting principle beyond quantum mechanics to broader non-classical theories, and also applies to steerable assemblages.

Contribution

It establishes the no-local-broadcasting theorem for nonlocal behaviors and assemblages using the monotonicity of relative entropy, confirming a key conjecture in the field.

Findings

Proved the no-local-broadcasting conjecture for nonlocal behaviors.

Derived an analogous no-go theorem for steerable assemblages.

Extended the no-broadcasting principle to broader non-classical theories.

Abstract

The no-broadcasting theorem is a fundamental result in quantum information theory. It guarantees that a class of attacks on quantum protocols, based on eavesdropping and indiscriminate copying of quantum information, are impossible. Due to its fundamental importance, it is natural to ask whether it is an intrinsic quantum property or whether it also holds for a broader class of non-classical theories. To address this question, one could use the framework of correlation scenarios. Under this standpoint, Joshi, Grudka, and the Horodeckis conjectured that one cannot locally broadcast nonlocal behaviours. In this paper, we prove their conjecture based on the monotonicity of the relative entropy for behaviours. Additionally, following a similar reasoning, we obtain an analogous no-go theorem for steerable assemblages.