The no-broadcast theorem says that, given a single copy of a state, it is impossible to create a state such that one part of it is the same as the original state and the other part is also the same as the original state. That is, given an initial state ${\displaystyle \rho _{1},}$ it is impossible to create a state ${\displaystyle \rho _{AB}}$ in a Hilbert space ${\displaystyle H_{A}\otimes H_{B}}$ such that the partial trace ${\displaystyle Tr_{A}\rho _{AB}=\rho _{1}}$ and ${\displaystyle Tr_{B}\rho _{AB}=\rho _{1}}$. Although here mixed states are considered, a broadcasting machine would have to work on any pure state ensemble of ${\displaystyle \rho _{1}.}$