Optimizing incompatible triple quantum measurements
Hui-Hui Qin, Shao-Ming Fei
TL;DR
This paper derives analytical expressions for the best possible joint measurements approximating triple incompatible qubit measurements, providing insights into quantum measurement uncertainty and potential experimental tests.
Contribution
It introduces analytical solutions for optimal joint approximations of triple incompatible qubit measurements, advancing understanding of quantum measurement uncertainty.
Findings
Derived analytical expressions for optimal joint measurements
Identified states minimizing measurement errors
Proposed experimental verification methods
Abstract
We investigate the optimal approximation to triple incompatible quantum measurements within the framework of statistical distance and joint measurability. According to the lower bound of the uncertainty inequality presented in [Physical Review A 99, 312107 (2019)], we give the analytical expressions of the optimal jointly measurable approximation to two kinds of triple incompatible unbiased qubit measurements. We also obtain the corresponding states which give the minimal approximation errors in measuring process. The results give rise to plausible experimental verifications of such statistical distance based uncertainty relations.
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