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

Simultaneous measurement of multiple observables {X1, X2, …, Xn} via a single measurement.

npj Quantum Information, Published online: 06 October 2024; doi:10.1038/s41534-024-00894-x

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

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.

A team of researchers has provided a framework to study the implementation of an arbitrary finite number of observables with a single measurement.

Their methodology yields novel analytical bounds on the errors of these implementations, significantly advancing our understanding of this fundamental problem.

Additionally, they introduced 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 their findings, they 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.

This work paves the way for optimizing various tasks in quantum information science that involve multiple noncommutative observables.

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