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

• URL: http://arxiv.org/abs/2211.14351v2
• Date: Fri, 10 Oct 2025 20:45:54 GMT
• Title: No-local-broadcasting theorem for non-signalling behaviours and assemblages
• Authors: Adrian Solymos, Carlos Vieira, Cristhiano Duarte, Zoltán Zimborás,
• Abstract summary: The no-broadcasting theorem is a fundamental result in quantum information theory.<n>We prove Joshi, Grudka, and Horodecki$otimes 4$ conjectured that one cannot locally broadcast nonlocal behaviours.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 Horodecki$^{\otimes 4}$ 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.

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