The understanding of open quantum systems is crucial for the development of quantum technologies. Of particular relevance is the characterisation of divisible quantum dynamics, seen as a generalisation of Markovian processes to the quantum setting. Here, we propose a way to detect divisibility and quantify how non-divisible a quantum channel is through the concept of channel discrimination. We ask how well we can distinguish generic dynamics from divisible dynamics. We show that this question can be answered efficiently through semidefinite programming, which provides us with an operational and efficient way to quantify divisibility.

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.