Randomized measurements for multi-parameter quantum metrology

• URL: http://arxiv.org/abs/2502.03536v1
• Date: Wed, 05 Feb 2025 19:00:04 GMT
• Title: Randomized measurements for multi-parameter quantum metrology
• Authors: Sisi Zhou, Senrui Chen,
• Abstract summary: We show that randomized measurements perform near-optimally when estimating an arbitrary number of parameters in pure states. The near-optimality is also shown in estimating the maximal number of parameters for three types of mixed states that are well-conditioned on its support.
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• Abstract: The optimal quantum measurements for estimating different unknown parameters in a parameterized quantum state are usually incompatible with each other. Traditional approaches to addressing the measurement incompatibility issue, such as the Holevo Cram\'{e}r--Rao bound, suffer from multiple difficulties towards practical applicability, as the optimal measurement strategies are usually state-dependent, difficult to implement and also take complex analyses to determine. Here we study randomized measurements as a new approach for multi-parameter quantum metrology. We show quantum measurements on single copies of quantum states given by 3-design perform near-optimally when estimating an arbitrary number of parameters in pure states and more generally, approximately low-rank states, whose metrological information is largely concentrated in a low-dimensional subspace. The near-optimality is also shown in estimating the maximal number of parameters for three types of mixed states that are well-conditioned on its support. Examples of fidelity estimation and Hamiltonian estimation are explicitly provided to demonstrate the power and limitation of randomized measurements in multi-parameter quantum metrology.

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