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1、Localhidden{variablemodelsforentangledquantumstatesRAugusiak1,MDemianowicz1,andAAcn1;21ICFO{InstitutdeCienciesFotoniques,MediterraneanTechnologyPark,08860Castelldefels(Barcelona),Spain2ICREA{InstitucioCatalanadeRecercaiEstudisAvancats,LluisCompanys23,08010Bar
2、celona,SpainAbstract.WhileentanglementandviolationofBellinequalitieswereinitiallythoughttobeequivalentquantumphenomena,wenowhavedi erentexamplesofentangledstateswhosecorrelationscanbedescribedbylocalhidden{variablemodelsand,therefore,donotviolateanyBellinequalit
3、y.Weprovideanuptodateoverviewoftheexistinglocalhidden{variablemodelsforentangledquantumstates,bothinthebipartiteandmultipartitecase,anddiscusssomeofthemostrelevantopenquestionsinthiscontext.Ourreviewcoverstwenty veyearsofthislineofresearchsincetheseminalworkbyWe
4、rner[R.F.Werner,Phys.Rev.A40,8(1989)]providingthe rstexampleofanentangledstatewithalocalmodel,whichinturnappearedtwenty veyearsaftertheseminalworkbyBell[J.S.Bell,Physics1,195(1964)],abouttheimpossibilityofrecoveringthepredictionsofquantummechanicsusingalocalhidd
5、en{variablestheory.arXiv:1405.7321v1[quant-ph]28May2014CONTENTS2Contents1Introduction22Preliminariesandnotation32.1Entanglement................................32.2Measurementinquantumtheory.....................32.3Bell-typeexperimentandlocalmodels...............
6、...53Bipartitequantumstates93.1Werner'smodel...............................103.2Barrett'smodelfortheWernerstates..................143.3Nonlocalityofnoisystates:theGrothendieckconstant.........173.4Noiserobustnessofcorrelations:Almeidaetal.'smodel........223.5Fro
7、mprojectivetogeneralizedmeasurements
8、Hirschetal.'sconstruction.................................274Multipartitequantumstates294.1LocalmodelforprojectivemeasurementsonGMEtripartitestates..294.2Generalizationsanddiscussion......................315Otherlocalityscena
9、rios326Conclusionsandoutlook33AppendixA351.IntroductionIn1935,theconceptsoflocal{hiddenvariablemodelandentanglementwereintroducedintheworksby,respectively,Einstein,Po
