The optimal approximations of available states and a triple uncertainty relation

Xiao-Bin Liang, Bo Li, Liang Huang, Biao-Liang Ye, Shao-Ming Fei, and Shi-Xiang Huang

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Submission date: 22. Jun. 2020
Pages: 9
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Abstract:
We investigate the optimal convex approximation of quantum state with respect to a set of available states. By isometric transformation, we have presented the general mathematical model and its solutions, together with a triple uncertainty equality relation. Meanwhile, we show a concise inequality criterion for decomposing qubit mixed states. The new results include previous ones as special cases. Our model and method may be applied to solve similar problems in high-dimensional and multipartite scenarios.