{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:47:00Z","timestamp":1760150820679,"version":"build-2065373602"},"reference-count":55,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,24]],"date-time":"2023-12-24T00:00:00Z","timestamp":1703376000000},"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":["11875086","11775019"],"award-info":[{"award-number":["11875086","11775019"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A quantum system interacting with a multipartite environment can induce redundant encoding of the information of a system into the environment, which is the essence of quantum Darwinism. At the same time, the environment may scramble the initially localized information about the system. Based on a collision model, we mainly investigate the relationship between information scrambling in an environment and the emergence of quantum Darwinism. Our results show that when the mutual information between the system and environmental fragment is a linear increasing function of the fragment size, the tripartite mutual information (TMI) is zero, which can be proved generally beyond the collision model; when the system exhibits Darwinistic behavior, the TMI is positive (i.e., scrambling does not occur); when we see the behavior of an \u201cencoding\u201d environment, the TMI is negative (i.e., scrambling occurs). Additionally, we give a physical explanation for the above results by considering two simple but illustrative examples. Moreover, depending on the nature of system and environment interactions, it is also shown that the single qubit and two-qubit systems behave differently for the emergence of quantum Darwinism, and hence the scrambling, while their relationship is consistent with the above conclusion.<\/jats:p>","DOI":"10.3390\/e26010019","type":"journal-article","created":{"date-parts":[[2023,12,24]],"date-time":"2023-12-24T20:42:30Z","timestamp":1703450550000},"page":"19","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Relationship between Information Scrambling and Quantum Darwinism"],"prefix":"10.3390","volume":"26","author":[{"given":"Feng","family":"Tian","sequence":"first","affiliation":[{"name":"School of Physics, Beijing Institute of Technology, Beijing 100081, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4127-8688","authenticated-orcid":false,"given":"Jian","family":"Zou","sequence":"additional","affiliation":[{"name":"School of Physics, Beijing Institute of Technology, Beijing 100081, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6577-2050","authenticated-orcid":false,"given":"Hai","family":"Li","sequence":"additional","affiliation":[{"name":"School of Information and Electronic Engineering, Shandong Technology and Business University, Yantai 264005, China"}]},{"given":"Liping","family":"Han","sequence":"additional","affiliation":[{"name":"School of Science, Tianjin University of Technology, Tianjin 300384, China"}]},{"given":"Bin","family":"Shao","sequence":"additional","affiliation":[{"name":"School of Physics, Beijing Institute of Technology, Beijing 100081, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1038\/nphys1202","article-title":"Quantum Darwinism","volume":"5","author":"Zurek","year":"2009","journal-title":"Nat. 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