Testing Heisenberg's measurement uncertainty relation of three
observables
- URL: http://arxiv.org/abs/2211.09389v2
- Date: Wed, 23 Nov 2022 07:58:18 GMT
- Title: Testing Heisenberg's measurement uncertainty relation of three
observables
- Authors: Ya-Li Mao, Hu Chen, Chang Niu, Zheng-Da Li, Sixia Yu, and Jingyun Fan
- Abstract summary: Heisenberg's measurement uncertainty relations (MUR) of two quantum observables are essential for quantum foundations and quantum information science.
We report the first experimental test of MURs for three quantum observables.
- Score: 3.021369108296711
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Heisenberg's measurement uncertainty relations (MUR) of two quantum
observables are essential for contemporary researches in quantum foundations
and quantum information science. Going beyond, here we report the first
experimental test of MURs for three quantum observables. Following the proposal
of Bush, Lahti, and Werner [Phys. Rev. A 89, 012129 (2014)], we first establish
rigorously MURs for triplets of unbiased qubit observables as combined
approximation errors lower-bounded by an incompatibility measure. We then
develop a convex programming protocol to numerically find the exact value of
the incompatibility measure and the corresponding optimal measurements.
Furthermore, we propose a novel implementation of optimal joint measurements
and experimentally test our MURs using a single-photon qubit. Lastly, we
discuss to analytically calculate the exact value of incompatibility measure
for some symmetric triplets. We anticipate that this work may stimulate broad
interests associated with the Heisenberg's uncertainty relation of multiple
observables, enriching our understanding of quantum mechanics and inspiring
innovative applications in quantum information science.
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