Probabilistic quantum cloning of three symmetric states

Abstract

This paper investigates the 1 → M probabilistic quantum cloning of three symmetric states, which are defined by a complex number of their inner product. First, a general transformation of the 1 → M probabilistic quantum cloning is designed, and the ancillary success states are introduced. Then, the explicit expression of the probability of successful cloning is derived, which depends on the number M and the inner product of the three symmetric states. Finally, three examples are provided to demonstrate the efficiency of our cloning transformation.