We study the probabilistic cloning of three symmetric states. These states are defined by a single complex quantity, the inner product among them. We show that three different probabilistic cloning machines are necessary to optimally clone all possible families of three symmetric states. We also show that the optimal cloning probability of generating $M$ copies out of one original can be cast as the quotient between the success probability of unambiguously discriminating one and $M$ copies of symmetric states.

• Received 18 October 2010

DOI:https://doi.org/10.1103/PhysRevA.82.062307