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

• URL: http://arxiv.org/abs/2109.05807v3
• Date: Mon, 27 Jun 2022 08:04:16 GMT
• Title: Incompatibility measures in multi-parameter quantum estimation under hierarchical quantum measurements
• Authors: Hongzhen Chen, Yu Chen, Haidong Yuan
• Abstract summary: We show an approach to study the incompatibility under general $p$-local measurements. We demonstrate the power of the approach by presenting a hierarchy of analytical bounds on the tradeoff.
• Score: 4.980960723762946
• License: http://creativecommons.org/licenses/by/4.0/
• 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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