{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:18:31Z","timestamp":1760235511360,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T00:00:00Z","timestamp":1630368000000},"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":["62072119, 61672007, 12075159"],"award-info":[{"award-number":["62072119, 61672007, 12075159"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["2020A1515011180"],"award-info":[{"award-number":["2020A1515011180"]}]},{"name":"Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology","award":["SIQSE202005, SIQSE202001"],"award-info":[{"award-number":["SIQSE202005, SIQSE202001"]}]},{"DOI":"10.13039\/100007219","name":"Natural Science Foundation of Shanghai","doi-asserted-by":"publisher","award":["20ZR1426400"],"award-info":[{"award-number":["20ZR1426400"]}],"id":[{"id":"10.13039\/100007219","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004826","name":"Beijing Natural Science Foundation","doi-asserted-by":"publisher","award":["Z190005"],"award-info":[{"award-number":["Z190005"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We show the properties and characterization of coherence witnesses. We show methods for constructing coherence witnesses for an arbitrary coherent state. We investigate the problem of finding common coherence witnesses for certain class of states. We show that finitely many different witnesses W1,W2,\u22ef,Wn can detect some common coherent states if and only if \u2211i=1ntiWi is still a witnesses for any nonnegative numbers ti(i=1,2,\u22ef,n). We show coherent states play the role of high-level witnesses. Thus, the common state problem is changed into the question of when different high-level witnesses (coherent states) can detect the same coherence witnesses. Moreover, we show a coherent state and its robust state have no common coherence witness and give a general way to construct optimal coherence witnesses for any comparable states.<\/jats:p>","DOI":"10.3390\/e23091136","type":"journal-article","created":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T08:42:32Z","timestamp":1630399352000},"page":"1136","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Common Coherence Witnesses and Common Coherent States"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0051-0081","authenticated-orcid":false,"given":"Bang-Hai","family":"Wang","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, Guangdong University of Technology, Guangzhou 510006, China"}]},{"given":"Zi-Heng","family":"Ding","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, China"},{"name":"Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China"}]},{"given":"Zhihao","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, China"},{"name":"Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2412-8626","authenticated-orcid":false,"given":"Shao-Ming","family":"Fei","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Capital Normal University, Beijing 100048, China"},{"name":"Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"041003","DOI":"10.1103\/RevModPhys.89.041003","article-title":"Colloquium: Quantum coherence as a resource","volume":"89","author":"Streltsov","year":"2017","journal-title":"Rev. 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