Novel cloning machine with supplementary information for copying quantum superposition of multiple clones

Probabilistic cloning was first proposed by Duan and Guo. Then Pati established a novel cloning machine (NCM) for copying quantum superposition of multiple clones. In this paper, we deal with the novel cloning machine with supplementary information (NCMSI) for obtaining quantum superposition of multiple clones. For the case of cloning two states, we demonstrate that the optimal efficiency of the NCMSI in which the original party and the supplementary party can perform quantum communication equals that achieved by a two-step cloning protocol wherein classical communication is only allowed between the original and the supplementary parties. From this equivalence it follows that NCMSI may increase the success probabilities for copying. Also, an upper bound on the unambiguous discrimination of two nonorthogonal pure produce states is derived. Our investigation generalizes and completes the result in the literature. PACS numbers: 03.67.-a, 03.65.Ud