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1、AbsolutelyMaximallyEntangledStates:ExistenceandApplicationsWolframHelwigandWeiCuiCenterforQuantumInformationandQuantumControl(CQIQC),DepartmentofPhysics,UniversityofToronto,Toronto,Ontario,M5S1A7,CanadaJune12,2013AbstractWeinvestigateabsolutelymaximallyentangled(AME
2、)states,whicharemultipartitequantumstatesthataremaximallyentangledwithre-specttoanypossiblebipartition.Thesestrongentanglementpropertiesmakethemapowerfulresourceforavarietyofquantuminformationpro-tocols.Inthispaper,weshowtheexistenceofAMEstatesforanynumberofparties,
3、giventhatthedimensionoftheinvolvedsystemsischosenap-propriately.WeprovetheequivalenceofAMEstatessharedbetweenanevennumberofpartiesandpurestatethresholdquantumsecretsharing(QSS)schemes,andprovenecessaryandsuciententanglementproper-tiesforawiderclassoframpQSSschemes.
4、WefurthershowhowAMEstatescanbeusedasavaluableresourceforopen-destinationteleporta-tionprotocolsandtowhatextendentanglementswappinggeneralizestoAMEstates.1IntroductionEntanglementhasbeenahottopicsincethebeginningofquantummechanicsandfueledalotofdiscussions,amongthemm
5、ostnotabletheEinstein-Podolsky-Rosen(EPR)paradox[1],which nallyledBelltocomeupwithamethodofactuallymeasuringentanglement[2].Itwasnotuntiltheadventofquantuminformation,however,thatentanglementwasrecognizedasausefulresource.Almostallapplicationsinquantuminformationmak
6、eeitherexplicitorimplicitarXiv:1306.2536v1[quant-ph]11Jun2013useofentanglement,whichmakesitcrucialtogainasmuchinsightaspossible.[3]Whiletheentanglementofbipartitestatesisalreadyverywellunderstood[4,5,6],theroadtoitsgeneralizationtomorethantwopartiesispavedwithmanyob
7、stacles.Thereforeweoftenhavetorestrictourselvestospecialcaseswhenanalyzingmultipartiteentanglement.Aprominentchoicearestatesthatextremizetheentanglementforacertainmeasureofentanglement.Inthispaperwewanttodothatbyfocusingonabsolutelymaximallyentangled(AME)states,whic
8、harede nedasstatesthataremaximallyentangledforanypossiblebipartition.[7,8,9]1De nition1.Anabsolutelymaximallyentangledstateisapurestate,sh
