{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T09:50:33Z","timestamp":1762509033292,"version":"build-2065373602"},"reference-count":48,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,17]],"date-time":"2023-10-17T00:00:00Z","timestamp":1697500800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Natural Science Foundation of China","award":["12004113","12034007","22ZR1418100","21XD1400700"],"award-info":[{"award-number":["12004113","12034007","22ZR1418100","21XD1400700"]}]},{"name":"the Natural Science Foundation of Shanghai","award":["12004113","12034007","22ZR1418100","21XD1400700"],"award-info":[{"award-number":["12004113","12034007","22ZR1418100","21XD1400700"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Quantum coherence is the most distinguished feature of quantum mechanics. As an important resource, it is widely applied to quantum information technologies, including quantum algorithms, quantum computation, quantum key distribution, and quantum metrology, so it is important to develop tools for efficient estimation of the coherence. Bell state measurement plays an important role in quantum information processing. In particular, it can also, as a two-copy collective measurement, directly measure the quantum coherence of an unknown quantum state in the experiment, and does not need any optimization procedures, feedback, or complex mathematical calculations. In this paper, we analyze the performance of estimating quantum coherence with Bell state measurement for a qubit case from the perspective of semiparametric estimation and single-parameter estimation. The numerical results show that Bell state measurement is the optimal measurement for estimating several frequently-used coherence quantifiers, and it has been demonstrated in the perspective of the quantum limit of semiparametric estimation and Fisher information.<\/jats:p>","DOI":"10.3390\/e25101459","type":"journal-article","created":{"date-parts":[[2023,10,17]],"date-time":"2023-10-17T10:43:10Z","timestamp":1697539390000},"page":"1459","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Optimal Estimation of Quantum Coherence by Bell State Measurement: A Case Study"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6215-9058","authenticated-orcid":false,"given":"Yuan","family":"Yuan","sequence":"first","affiliation":[{"name":"School of Physics, East China University of Science and Technology, Shanghai 200237, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xufeng","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Physics, East China University of Science and Technology, Shanghai 200237, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yueping","family":"Niu","sequence":"additional","affiliation":[{"name":"School of Physics, East China University of Science and Technology, Shanghai 200237, China"},{"name":"Shanghai Engineering Research Center of Hierarchical Nanomaterials, Shanghai 200237, China"},{"name":"Shanghai Frontiers Science Center of Optogenetic Techniques for Cell Metabolism, Shanghai 200237, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shangqing","family":"Gong","sequence":"additional","affiliation":[{"name":"School of Physics, East China University of Science and Technology, Shanghai 200237, China"},{"name":"Shanghai Engineering Research Center of Hierarchical Nanomaterials, Shanghai 200237, China"},{"name":"Shanghai Frontiers Science Center of Optogenetic Techniques for Cell Metabolism, Shanghai 200237, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1103\/RevModPhys.81.865","article-title":"Quantum entanglement","volume":"81","author":"Horodecki","year":"2009","journal-title":"Rev. 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