We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
67/2020
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
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.
