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arXiv · 2109.05807

Incompatibility measures in multi-parameter quantum estimation under hierarchical quantum measurements

Hongzhen Chen·Yu Chen·Haidong Yuan
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Abstract

The incompatibility of the measurements constraints the achievable precisions in multi-parameter quantum estimation. Understanding the tradeoff induced by such incompatibility is a central topic in quantum metrology. Here we provide an approach to study the incompatibility under general $p$-local measurements, which are the measurements that can be performed collectively on at most $p$ copies of quantum states. We demonstrate the power of the approach by presenting a hierarchy of analytical bounds on the tradeoff among the precision limits of different parameters. These bounds lead to a necessary condition for the saturation of the quantum Cram\'er-Rao bound under $p$-local measurements, which recovers the partial commutative condition at p=1 and the weak commutative condition at $p=\infty$. As a further demonstration of the power of the framework, we present another set of tradeoff relations with the right logarithmic operators(RLD).

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Hongzhen Chen, Yu Chen, Haidong Yuan. 2021-09-13. Incompatibility measures in multi-parameter quantum estimation under hierarchical quantum measurements. https://doi.org/10.1103/physreva.105.062442

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