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
TL;DR
This paper develops a mathematical framework for optimally approximating quantum states using available states, introduces a triple uncertainty relation, and provides criteria for decomposing qubit mixed states, with potential applications in complex quantum systems.
Contribution
It presents a general mathematical model for optimal convex approximation of quantum states and introduces a novel triple uncertainty equality relation, extending previous results.
Findings
Derived a general mathematical model for state approximation
Established a triple uncertainty equality relation
Provided a criterion for decomposing qubit mixed states
Abstract
We investigate the optimal convex approximation of the 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
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