Simultaneous measurement of multiple incompatible observables and tradeoff in multiparameter quantum estimation

IF 6.6 1区 物理与天体物理 Q1 PHYSICS, APPLIED npj Quantum Information Pub Date : 2024-10-06 DOI:10.1038/s41534-024-00894-x
Hongzhen Chen, Lingna Wang, Haidong Yuan
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Abstract

How well can multiple incompatible observables be implemented by a single measurement? This is a fundamental problem in quantum mechanics with wide implications for the performance optimization of numerous tasks in quantum information science. While existing studies have been mostly focusing on the approximation of two observables with a single measurement, in practice multiple observables are often encountered, for which the errors of the approximations are little understood. Here we provide a framework to study the implementation of an arbitrary finite number of observables with a single measurement. Our methodology yields novel analytical bounds on the errors of these implementations, significantly advancing our understanding of this fundamental problem. Additionally, we introduce a more stringent bound utilizing semi-definite programming that, in the context of two observables, generates an analytical bound tighter than previously known bounds. The derived bounds have direct applications in assessing the trade-off between the precision of estimating multiple parameters in quantum metrology, an area with crucial theoretical and practical implications. To validate the validity of our findings, we conducted experimental verification using a superconducting quantum processor. This experimental validation not only confirms the theoretical results but also effectively bridges the gap between the derived bounds and empirical data obtained from real-world experiments. Our work paves the way for optimizing various tasks in quantum information science that involve multiple noncommutative observables.

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多参数量子估算中多个不兼容观测变量的同时测量与权衡
一次测量能在多大程度上实现多个不兼容的观测值?这是量子力学中的一个基本问题,对量子信息科学中众多任务的性能优化具有广泛影响。现有的研究主要集中在用单次测量近似两个观测值,而在实际应用中经常会遇到多个观测值,对于这些观测值的近似误差却知之甚少。在这里,我们提供了一个框架,研究用一次测量实现任意有限数量的观测值。我们的方法对这些实现的误差产生了新的分析界限,极大地推动了我们对这一基本问题的理解。此外,我们还利用半有限编程引入了更严格的约束,在两个观测变量的情况下,产生的分析约束比以前已知的约束更严格。推导出的边界可直接用于评估量子计量学中多个参数估计精度之间的权衡,这是一个具有重要理论和实践意义的领域。为了验证我们研究结果的有效性,我们使用超导量子处理器进行了实验验证。这一实验验证不仅证实了理论结果,还有效地弥合了推导边界与实际实验中获得的经验数据之间的差距。我们的工作为优化量子信息科学中涉及多个非交换观测变量的各种任务铺平了道路。
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来源期刊
npj Quantum Information
npj Quantum Information Computer Science-Computer Science (miscellaneous)
CiteScore
13.70
自引率
3.90%
发文量
130
审稿时长
29 weeks
期刊介绍: The scope of npj Quantum Information spans across all relevant disciplines, fields, approaches and levels and so considers outstanding work ranging from fundamental research to applications and technologies.
期刊最新文献
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