Measurement uncertainty relation for three observables
- URL: http://arxiv.org/abs/2211.09816v3
- Date: Thu, 24 Nov 2022 02:12:59 GMT
- Title: Measurement uncertainty relation for three observables
- Authors: Sixia Yu, Ya-Li Mao, Chang Niu, Hu Chen, Zheng-Da Li, and Jingyun Fan
- Abstract summary: We establish a measurement uncertainty relation (MUR) for three unbiased qubit observables.
We derive a necessary and sufficient condition for the triplet MUR to be saturated and the corresponding optimal measurement.
- Score: 3.021369108296711
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: In this work we establish rigorously a measurement uncertainty relation (MUR)
for three unbiased qubit observables, which was previously shown to hold true
under some presumptions. The triplet MUR states that the uncertainty, which is
quantified by the total statistic distance between the target observables and
the jointly implemented observables, is lower bounded by an incompatibility
measure that reflects the joint measurement conditions. We derive a necessary
and sufficient condition for the triplet MUR to be saturated and the
corresponding optimal measurement. To facilitate experimental tests of MURs we
propose a straightforward implementation of the optimal joint measurements. The
exact values of incompatibility measure are analytically calculated for some
symmetric triplets when the corresponding triplet MURs are not saturated. We
anticipate that our work may enrich the understanding of quantum
incompatibility in terms of MURs and inspire further applications in quantum
information science. This work presents a complete theory relevant to a
parallel work [Y.-L. Mao, et al., Testing Heisenberg's measurement uncertainty
relation of three observables, arXiv:2211.09389] on experimental tests.
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