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 nonclassical 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 behaviors. In this paper, we prove their conjecture based on the monotonicity of the relative entropy for behaviors. Additionally, following a similar reasoning, we obtain an analogous no-go theorem for steerable assemblages.

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• Quantum correlations in quantum information
• Quantum correlations, foundations & formalism
• Quantum foundations