{"title":"Alternative to purification in conformal field theory","authors":"Xin Jiang, Peng Wang, Houwen Wu, Haitang Yang","doi":"10.1103/physrevd.111.l021902","DOIUrl":null,"url":null,"abstract":"In conformal field theories, in contrast to some auxiliary states into the bipartite mixed state ρ</a:mi>A</a:mi>B</a:mi></a:mrow></a:msub></a:math> as the usual purifications do, we show a pure entangled state <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><c:msub><c:mi>ψ</c:mi><c:mrow><c:mi>A</c:mi><c:mi>B</c:mi></c:mrow></c:msub></c:math> can be constructed by the undetectable regions. In this pure state <e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><e:msub><e:mi>ψ</e:mi><e:mrow><e:mi>A</e:mi><e:mi>B</e:mi></e:mrow></e:msub></e:math>, the von Neumann entropy <g:math xmlns:g=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><g:msub><g:mi>S</g:mi><g:mi>vN</g:mi></g:msub><g:mo stretchy=\"false\">(</g:mo><g:mi>A</g:mi><g:mo>:</g:mo><g:mi>B</g:mi><g:mo stretchy=\"false\">)</g:mo></g:math> naturally captures quantum entanglement between <k:math xmlns:k=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><k:mi>A</k:mi></k:math> and <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><m:mi>B</m:mi></m:math>. We verify that <o:math xmlns:o=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><o:msub><o:mi>S</o:mi><o:mi>vN</o:mi></o:msub><o:mo stretchy=\"false\">(</o:mo><o:mi>A</o:mi><o:mo>:</o:mo><o:mi>B</o:mi><o:mo stretchy=\"false\">)</o:mo></o:math> is equal to the entanglement wedge cross section <s:math xmlns:s=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><s:msub><s:mi>E</s:mi><s:mi>W</s:mi></s:msub></s:math> in anti–de Sitter spacetime, which is conjectured to be the holographic dual of the entanglement of purification. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20167,"journal":{"name":"Physical Review D","volume":"9 1","pages":""},"PeriodicalIF":5.0000,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review D","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevd.111.l021902","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 0
Abstract
In conformal field theories, in contrast to some auxiliary states into the bipartite mixed state ρAB as the usual purifications do, we show a pure entangled state ψAB can be constructed by the undetectable regions. In this pure state ψAB, the von Neumann entropy SvN(A:B) naturally captures quantum entanglement between A and B. We verify that SvN(A:B) is equal to the entanglement wedge cross section EW in anti–de Sitter spacetime, which is conjectured to be the holographic dual of the entanglement of purification. Published by the American Physical Society2025
期刊介绍：
Physical Review D (PRD) is a leading journal in elementary particle physics, field theory, gravitation, and cosmology and is one of the top-cited journals in high-energy physics.
PRD covers experimental and theoretical results in all aspects of particle physics, field theory, gravitation and cosmology, including:
Particle physics experiments,
Electroweak interactions,
Strong interactions,
Lattice field theories, lattice QCD,
Beyond the standard model physics,
Phenomenological aspects of field theory, general methods,
Gravity, cosmology, cosmic rays,
Astrophysics and astroparticle physics,
General relativity,
Formal aspects of field theory, field theory in curved space,
String theory, quantum gravity, gauge/gravity duality.
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