{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:53:05Z","timestamp":1760147585641,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,15]],"date-time":"2023-02-15T00:00:00Z","timestamp":1676419200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11805010","12175014","92265115"],"award-info":[{"award-number":["11805010","12175014","92265115"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>As the connection between classical and quantum worlds, quantum measurements play a unique role in the era of quantum information processing. Given an arbitrary function of quantum measurements, how to obtain its optimal value is often considered as a basic yet important problem in various applications. Typical examples include but are not limited to optimizing the likelihood functions in quantum measurement tomography, searching the Bell parameters in Bell-test experiments, and calculating the capacities of quantum channels. In this work, we propose reliable algorithms for optimizing arbitrary functions over the space of quantum measurements by combining the so-called Gilbert\u2019s algorithm for convex optimization with certain gradient algorithms. With extensive applications, we demonstrate the efficacy of our algorithms with both convex and nonconvex functions.<\/jats:p>","DOI":"10.3390\/e25020358","type":"journal-article","created":{"date-parts":[[2023,2,15]],"date-time":"2023-02-15T03:37:24Z","timestamp":1676432244000},"page":"358","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Reliable Optimization of Arbitrary Functions over Quantum Measurements"],"prefix":"10.3390","volume":"25","author":[{"given":"Jing","family":"Luo","sequence":"first","affiliation":[{"name":"Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement of Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2332-5882","authenticated-orcid":false,"given":"Jiangwei","family":"Shang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement of Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2009.02.004","article-title":"Entanglement detection","volume":"474","year":"2009","journal-title":"Phys. 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