Quantum information becomes classical when distributed to many users

Abstract

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(err) > or = 0.45 in distinguishing classical from quantum output, a value close to the error probability of the random guess.