Quantum Information Becomes Classical When Distributed to Many Users

Any physical transformation that equally distributes quantum information over a large number $M$ of users can be approximated by a classical broadcasting of measurement outcomes. The accuracy of the approximation is at least of the order $O(M^{-1})$. In particular, quantum cloning of pure and mixed states can be approximated via quantum state estimation. As an example, for optimal qubit cloning with 10 output copies, a single user has an error probability $p_{\mathrm{err}}\ge 0.45$ in distinguishing classical from quantum output, a value close to the error probability of the random guess.