Liu Q, Hu Z, Yuan H, Yang Y. Optimal Strategies of Quantum Metrology with a Strict Hierarchy.
PHYSICAL REVIEW LETTERS 2023;
130:070803. [PMID:
36867832 DOI:
10.1103/physrevlett.130.070803]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Revised: 10/08/2022] [Accepted: 01/17/2023] [Indexed: 06/18/2023]
Abstract
One of the main quests in quantum metrology is to attain the ultimate precision limit with given resources, where the resources are not only of the number of queries, but more importantly of the allowed strategies. With the same number of queries, the restrictions on the strategies constrain the achievable precision. In this Letter, we establish a systematic framework to identify the ultimate precision limit of different families of strategies, including the parallel, the sequential, and the indefinite-causal-order strategies, and provide an efficient algorithm that determines an optimal strategy within the family of strategies under consideration. With our framework, we show there exists a strict hierarchy of the precision limits for different families of strategies.
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