目标态与给定量子态集合的最佳近似
The best approximation of an objective state with a given set of quantum states
摘要：
用一些已知态的凸混合近似一个量子态具有很强的实验意义，并在量子资源理论中提供了潜在的应用。本文给出了d维目标量子态与被限制在任意给定（混合）态集中的量子态凸混合的量子态之间在l_2范数意义下的最小距离的封闭形式。特别是，我们提出了最小数量的状态在给定的集合中，以实现最佳的距离。通过几个随机产生的量子态的数值计算，进一步验证了封闭解的有效性。
英文摘要：
Approximating a quantum state by the convex mixing of some given states has strong experimental significance and provides potential applications in quantum resource theory. Here we find a closed form of the minimal distance in the sense of l_2 norm between a given d-dimensional objective quantum state and the state convexly mixed by those restricted in any given (mixed-) state set. In particular, we present the minimal number of the states in the given set to achieve the optimal distance. The validity of our closed solution is further verified numerically by several randomly generated quantum states.
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