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1、DynamicsofquantumentanglementKarolZyczkowski˙1,2∗,PawelHorodecki3,∗∗,MichalHorodecki4,∗∗∗,RyszardHorodecki4,‡1CentrumFizykiTeoretycznejPAN,Al.Lotnik´ow32/46,02-668Warszawa,Poland2InstytutFizykiim.Smoluchowskiego,UniwersytetJagiello´nski,ul.Reymonta4,30-059Krak´ow,
2、Poland3WydzialFizykiTechnicznejiMatematykiStosowanej,PolitechnikaGda´nska,80–952Gda´nsk,Poland4InstytutFizykiTeoretycznejiAstrofizyki,UniwersytetGda´nski,80–952Gda´nsk,Polandment.WedemonstrateapossiblepresenceofrevivalsofAmodelofdiscretedynamicsofentanglementofbipa
3、rtiteentanglementcausedbytheglobalunitaryevolutionen-quantumstateisconsidered.Itinvolvesaglobalunitarydy-tanglingthesubsystemsbetweenconsecutiveactionsofnamicsofthesystemandperiodicactionsoflocalbistochastictheenvironment.ordecayingchannel.Forinitiallypurestatesth
4、edecayofen-Thepaperisorganisedasfollows.InsectionIIwetanglementisaccompaniedwithanincreaseofvonNeumanndescribeasimplemodelofdiscretetimeevolution.Inentropyofthesystem.WeobserveanddiscussrevivalsofsectionIIIwederiveboundsontheentropyincreaseun-entanglementduetounit
5、aryinteractionofsubsystems.Fordertheactionoftheenvironment.TheninsectionIVsomemixedstateshavingdifferentmarginalentropiesofthesubsystemswefindanasymmetryinspeedofentanglementweanalysethedecreaseofentanglementversusincreasedecay.Theentanglementofthesestatesdecreasesf
6、aster,ifofthedegreeofmixingoftheinitiallypurestates.Thethedepolarizingchannelactsonthe”classical”subsystem,asymmetryintheentanglementdecaydependingonthecharacterizedbysmallermarginalentropy.subsystemsubjectingtoinfluenceofenvironmentisde-scribedinsectionV.Insection
7、VIweconsidertheentan-PACSnumbers:03.65Bz,03.67.-aglementrevivals.TheresultsofthepaperarediscussedinsectionVII.I.INTRODUCTIONII.MODELSOFTIMEEVOLUTIONQuantumentanglementisoneofthemostsubtleandInthispaperweconsiderthebipartitestatesubjectedintriguingphenomenainnature
8、[1,2].Itspotentialuse-sequentialinteractionswithenvironment.Theyaremod-fulnesshasbeendemonstratedinvariousapplicationselledbyquantumchannels,definedascom
