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

Abstract

We investigate the cases where a set $S$ of states $\{|{\psi }_i⟩\}$ 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.

4 pages, 1 figure