Quantum cloning with nonlocal assistance: Complement of Jozsa's stronger no-cloning theorem

We investigate the cases where a set $S$ of states $\{\ket{\psi_i} \}$ cannot be cloned by itself, but is clonable with the help of another system prepared in state $\hat{\rho}_i$. When $S$ is pair-wise nonorthogonal, it is known that one can generate the copy from $\hat{\rho}_i$ alone, with no interaction with the original system. Here we show that a set containing orthogonal pairs exhibits a property forming a striking contrast; For any such set, there is a choice of $\hat{\rho}_i$ that enables cloning only when the two systems are interacted in a purely quantum manner that is not achievable via classical communication.