Related Experiment Video
Updated: Jul 12, 2025

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source
Published on: April 4, 2017
Testing Heisenberg-Type Measurement Uncertainty Relations of Three Observables
Ya-Li Mao1, Hu Chen1,2, Chang Niu3
1Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen, 518055, China.
Abstract:
Heisenberg-type measurement uncertainty relations (MURs) of two quantum observables are essential for contemporary research in quantum foundations and quantum information science. Going beyond, here we report the first experimental study of MUR of three quantum observables. We establish rigorously MURs for triplets of unbiased qubit observables as combined approximation errors lower bounded by an incompatibility measure, inspired by the proposal of Busch et al. [Phys. Rev. A 89, 012129 (2014)PLRAAN1050-294710.1103/PhysRevA.89.012129]. We develop a convex programming protocol to numerically find the exact value of the incompatibility measure and the optimal measurements. We propose a novel implementation of the optimal joint measurements and present several experimental demonstrations with a single-photon qubit. We stress that our method is universally applicable to the study of many qubit observables. Besides, we theoretically show that MURs for joint measurement can be attained by sequential measurements in two of our explored cases. We anticipate that this work may stimulate broad interests associated with Heisenberg's uncertainty principle in the case of multiple observables, enriching our understanding of quantum mechanics and inspiring innovative applications in quantum information science.
Related Concept Videos
The Uncertainty Principle
Uncertainty in Measurement: Reading Instruments
Uncertainty: Overview
Uncertainty in Measurement: Accuracy and Precision
Propagation of Uncertainty from Random Error
Propagation of Uncertainty from Systematic Error

