Physical accessible transformations on a finite number of quantum states
Xiang-Fa Zhou, Qing Lin, Yong-Sheng Zhang, Guang‐Can Guo · Physical Review A · 2007
We consider treating the usual probabilistic cloning, state separation, unambiguous state discrimination, etc., in a uniform framework. All these transformations can be regarded as special examples of generalized completely positive trace-nonincreasing maps on a finite number of input states. From the system-ancilla model we construct the corresponding unitary implementation of $\text{pure}\ensuremath{\rightarrow}\text{pure}$, $\text{pure}\ensuremath{\rightarrow}\text{mixed}$, $\text{mixed}\ensuremath{\rightarrow}\text{pure}$, and $\text{mixed}\ensuremath{\rightarrow}\text{mixed}$ state transformations in the whole system and obtain the necessary and sufficient conditions for the existence of the desired maps. We expect our work will be helpful to explore physically accessible transormations on a finite set of input states.