Upper bound on the success probability of separation among quantum states

Quantum state separation is a more general operation for identifying states than unambiguous discrimination. In this paper, we derive an upper bound on the success probability of separation among n states with arbitrary a priori probabilities, extending some of the important results given in the literature. This conclusion generalizes that obtained by Chefles and Barnett for separating two states having equal a priori probabilities. Some of the known bounds on the success probabilities of unambiguous discrimination such as the Ivanovic–Dieks–Peres limit, the more general limit by Jaeger and Shimony, and an upper bound for the case of unambiguously discriminating n states, are special cases of our results. Notably, we also give implicitly a different method to derive the upper bound on the probability of successful unambiguous discrimination among n states. Finally, we apply our conclusion to quantum cloning and then derive some upper bounds on the success probabilities for several probabilistic cloning machines.