{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:02:22Z","timestamp":1760238142773,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,20]],"date-time":"2022-07-20T00:00:00Z","timestamp":1658275200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Guangdong Province of China","award":["2021A1515011440","2019B030302008","62032009","2021CXB007"],"award-info":[{"award-number":["2021A1515011440","2019B030302008","62032009","2021CXB007"]}]},{"name":"Major Program of Guangdong Basic and Applied Research","award":["2021A1515011440","2019B030302008","62032009","2021CXB007"],"award-info":[{"award-number":["2021A1515011440","2019B030302008","62032009","2021CXB007"]}]},{"name":"National Natural Science Foundation of China","award":["2021A1515011440","2019B030302008","62032009","2021CXB007"],"award-info":[{"award-number":["2021A1515011440","2019B030302008","62032009","2021CXB007"]}]},{"name":"Outstanding Innovative Talents Cultivation Funded Programs for Doctoral Students of Jinan University","award":["2021A1515011440","2019B030302008","62032009","2021CXB007"],"award-info":[{"award-number":["2021A1515011440","2019B030302008","62032009","2021CXB007"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Quantum verification has been highlighted as a significant challenge on the road to scalable technology, especially with the rapid development of quantum computing. To verify quantum states, self-testing is proposed as a device-independent concept, which is based only on the observed statistics. Previous studies focused on bipartite states and some multipartite states, including all symmetric states, but only in the case of three qubits. In this paper, we first give a criterion for the self-testing of a four-qubit symmetric state with a special structure and the robustness analysis based on vector norm inequalities. Then we generalize the idea to a family of parameterized four-qubit symmetric states through projections onto two subsystems.<\/jats:p>","DOI":"10.3390\/e24071003","type":"journal-article","created":{"date-parts":[[2022,7,20]],"date-time":"2022-07-20T11:22:24Z","timestamp":1658316144000},"page":"1003","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Robust Self-Testing of Four-Qubit Symmetric States"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9377-0009","authenticated-orcid":false,"given":"Daipengwei","family":"Bao","sequence":"first","affiliation":[{"name":"School of Information Science and Technology, Jinan University, Guangzhou 510632, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3303-2493","authenticated-orcid":false,"given":"Xiaoqing","family":"Tan","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Jinan University, Guangzhou 510632, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5506-1933","authenticated-orcid":false,"given":"Qingshan","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Jinan University, Guangzhou 510632, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haozhen","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Jinan University, Guangzhou 510632, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8439-4526","authenticated-orcid":false,"given":"Rui","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Jinan University, Guangzhou 510632, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1655","DOI":"10.1098\/rsta.2003.1227","article-title":"Quantum technology: The second quantum revolution","volume":"361","author":"Dowling","year":"2003","journal-title":"Philos. 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