Alternative derivation of the criterion for economical realization of one-to-two qubit cloning

Abstract

In a previous paper [Phys. Rev. A 69 (2004) 062316], two of us (JD and TD) derived a necessary and sufficient condition for the reducibility of 3 qubit one-to-two cloners to 2 qudit one-to-two cloners. When this criterion is fulfilled, economical cloning is possible. We show in the present paper how to generalize the assumptions under which this condition is valid. We also extend this result to qudit one-to-two cloners, with d finite but arbitrary. © 2006 World Scientific Publishing Company.