{"title":"Entropic relations for indistinguishable quantum particles","authors":"Marius Lemm","doi":"10.1088/1742-5468/ad343a","DOIUrl":null,"url":null,"abstract":"The von Neumann entropy of a <italic toggle=\"yes\">k</italic>-body-reduced density matrix <italic toggle=\"yes\">γ</italic>\n<sub>\n<italic toggle=\"yes\">k</italic>\n</sub> quantifies the entanglement between <italic toggle=\"yes\">k</italic> quantum particles and the remaining ones. In this paper, we rigorously prove general properties of this entanglement entropy as a function of <italic toggle=\"yes\">k</italic>; it is concave for all <inline-formula>\n<tex-math><?CDATA $1\\unicode{x2A7D} k\\unicode{x2A7D} N$?></tex-math>\n<mml:math overflow=\"scroll\"><mml:mrow><mml:mn>1</mml:mn><mml:mtext>⩽</mml:mtext><mml:mi>k</mml:mi><mml:mtext>⩽</mml:mtext><mml:mi>N</mml:mi></mml:mrow></mml:math>\n<inline-graphic xlink:href=\"jstatad343aieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> and non-decreasing until the midpoint <inline-formula>\n<tex-math><?CDATA $k\\unicode{x2A7D} \\lfloor{N/2} \\rfloor$?></tex-math>\n<mml:math overflow=\"scroll\"><mml:mrow><mml:mi>k</mml:mi><mml:mtext>⩽</mml:mtext><mml:mo fence=\"false\" stretchy=\"false\">⌊</mml:mo><mml:mrow><mml:mi>N</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mo fence=\"false\" stretchy=\"false\">⌋</mml:mo></mml:mrow></mml:math>\n<inline-graphic xlink:href=\"jstatad343aieqn2.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>. The results hold for indistinguishable quantum particles and are independent of the statistics.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Mechanics: Theory and Experiment","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1742-5468/ad343a","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
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Abstract
The von Neumann entropy of a k-body-reduced density matrix γk quantifies the entanglement between k quantum particles and the remaining ones. In this paper, we rigorously prove general properties of this entanglement entropy as a function of k; it is concave for all 1⩽k⩽N and non-decreasing until the midpoint k⩽⌊N/2⌋. The results hold for indistinguishable quantum particles and are independent of the statistics.
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