Optimizing incompatible triple quantum measurements

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.

8 pages, 3 figures

References in corpus (9)

• Heisenberg's Uncertainty Principle
• Stronger uncertainty relations for the sum of variances
• Entropic uncertainty relations for multiple measurements
• Sum Uncertainty Relation in Quantum Theory
• Heisenberg Uncertainty Relation for Three Canonical Observables
• Multi-observable Uncertainty Relations in Product Form of Variances
• Error-Disturbance Trade-off in Sequential Quantum Measurements
• Uncertainties of genuinely incompatible triple measurements based on statistical distance
• Optimal Universal Uncertainty Relations