论文标题
三个可观察的测量不确定性关系
Measurement uncertainty relation for three observables
论文作者
论文摘要
在这项工作中，我们严格地建立了三个无偏量子观测值的测量不确定性关系（MUR），以前证明在某些推定下可以保持真实。三胞胎MUR指出，通过目标可观察物与共同实现的观测值之间的总统计距离量化的不确定性是由反映关节测量条件的不兼容度量的下限。我们得出了使三胞胎MUR饱和和相应的最佳测量的必要条件。为了促进MURS的实验测试，我们提出了最佳关节测量值的直接实施。当相应的三重态MUR未饱和时，通过分析对某些对称三重态的不兼容度量的确切值进行分析计算。我们预计我们的工作可能会在Murs方面丰富对量子不相容性的理解，并激发量子信息科学中的进一步应用。这项工作提出了与平行工作相关的完整理论[Y.-L。 Mao等人，在实验测试中测试了海森堡的测量不确定性关系，三个可观察到的arxiv：2211.09389]。
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.
