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1、MIT-CTP-4749ExperimentaltestofentangledhistoriesJordanCotler,1Lu-MingDuan,2,3,Pan-YuHou,2FrankWilczek,4,5DaXu,2,6Zhang-QiYin,2,yandChongZu21StanfordInstituteforTheoreticalPhysics,DepartmentofPhysics,StanfordUniversity2CenterforQuantumInformation,InstituteforI
2、nterdisciplinaryInformationSciences,TsinghuaUniversity,Beijing100084,China3DepartmentofPhysics,UniversityofMichigan,AnnArbor,Michigan48109,USA4CenterforTheoreticalPhysics,MIT,CambridgeMA02139USA5OriginsProject,ArizonaStateUniversity,TempeAZ25287USA6Departmento
3、fPhysics,TsinghuaUniversity,Beijing100084,ChinaAbstractWeproposeanddemonstrateexperimentallyaschemetocreateentangledhistorystatesoftheGreenberger-Horne-Zeilinger(GHZ)type.Inourexperiment,thepolarizationstatesofasinglephotonatthreedierenttimesarepreparedasaGHZe
4、ntangledhistorystate.WedefineaGHZfunctionalwhichattainsamaximumvalue1ontheidealGHZentangledhistorystateandisboundedaboveby1=16foranythree-timehistorystatelackingtripartiteentanglement.WehavemeasuredtheGHZfunctionalonastatewehavepreparedexperimentally,yieldingav
5、alueof0:6560:005,clearlydemonstratingthecontributionofentangledhistories.arXiv:1601.02943v2[quant-ph]20Jan2016lmduan@umich.eduyyinzhangqi@mail.tsinghua.edu.cn1I.INTRODUCTIONThetraditional“observables”ofquantumtheoryareoperatorsinHilbertspacethatactatapar-R2t
6、iculartime.Butmanyquantitiesofphysicalinterest,suchastheaccumulatedphaseexpidt~vA~1ofaparticlemovinginanelectromagneticpotential,oritsaccumulatedpropertime,aremorenat-urallyexpressedintermsofhistories.Wemayask:Havingperformedameasurementofthismoregeneral,hist
7、ory-dependentsortofobservable,whathavewelearned?Forconventionalob-servables,theansweristhatwelearnoursystemisinaparticularsubspaceofHilbertspace,thatis,theeigenspacecorrespondingtotheobservable’smeasuredvalue.Recentlytwoofus,buildingontheworkofGrithsandothers
8、[1],haveformulatedamath-ematicalframeworkwhichextendsmanyoftheconceptsandproceduresordinarilyusedinana-lyzingstatesofquantumsystemstotheirhistories[2–4].Specifically,wehaveconstruct
