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The no-broadcast theorem is a result in quantum information theory. In the case of pure quantum states, it is a corollary of the no cloning theorem: since quantum states cannot be copied in general, they cannot be broadcast. For mixed states, it generalizes no-cloning. The no-cloning theorem says that it is impossible to create two copies of a state given a single copy of the state. The no-broadcast theorem says that given a single copy of a state, it is impossible to create a state such that part of it is the same as the original state, and the other part is also the same as the original state. I.e. given an initial state $rho_1$ it is impossible to create a state $rho_\left\{AB\right\}$ such that $Tr_Arho_\left\{AB\right\}=rho_1$ and $Tr_Brho_\left\{AB\right\}=rho_1$. Although here we work with mixed states, a broadcasting machine would have to work on any pure state ensemble of $rho_1$.