利用基本不等式,给出在任意先验概率下,两个量子态的概率m→n量子克隆的平均失败概率具体表达式。结果表明当拷贝的数目趋近无穷大时,概率量子克隆收敛为最优确定性量子态区分。平均失败概率依赖于先验概率,使得在一定的先验概率下总有一个量子态的拷贝不能获得。通过提高平均失败概率,在任意先验概率下总可以获得两个量子态的拷贝。

By exploring the basic inequality, the explicit expression of the average failure probability of the probabilistic m→n quantum cloning of two quantum states with arbitrary a prior probability is given. Results show that when the number of copies approaches infinity, the probabilistic quantum cloning converges to the optimal unambiguous quantum state discrimination. The average failure probability depends on a prior probability, which makes the copies of one of two states can not be always obtained for some a prior probability. By enhancing the average failure probability, the copies of two states can be always obtained for arbitrary a prior probability.