Bell-Measurements-and-Teleportation英语教学课件

BellMeasurementsandTeleportationOverviewEntanglementBellstatesandBellmeasurementsLimitationsonBellmeasurementsusinglineardevicesTeleportationDensecodingEntanglementswappingEntanglementpurificationQuantumrepeatersEntanglementTwosystemsdescribedbytwoseparableHilbertspaces.Statesofthetwosystemscanbedescribedbythetensorproduct oftheirstatespaces.Schmidtdecomposition:If andthestateissaidtobeseparable.Ifmorethanonethenissaidtobeentangled.Thestateofonesystemcannotbespecifiedwithouttheother.BellStatesFortwotwo-statesystemsdenotedeachby theBellstatesformabasisforthewholesystemandaremaximallyentangled: whereisanti-symmetricandaresymmetricwithrespecttoparticleinterchanging.BellMeasurementsDistinguishingBellstatesusinglinearelementssuchasbeamsplitters,phaseshifters,photo-detectorsetc.Allelementscanbedescribedbyunitarytransformations.Inlinearonesparticlenumberisconserved.PolarizationbeamsplitterHalfwaveplateat45degreesExamplesforphotons:

Beamsplitter:Example:distinguishinganti-symmetricandsymmetricstates-Hong–Ou–MandeleffectDoubletransmissionobtainsaminussignrelativetodoublereflection.symmetricstateshavezeroamplitudeford1-d2coincidence.d1+d2simultaneous“click”thestatehascollapsedto

BymeasuringtheBelloperatorwehavecreatedentanglement!Beamsplitteroperatorrepresentationforasinglephoton:OR?DistinguishingBellStatesThegoal:Tocreateasetofunitaryoperatorsthatwouldmakeadifferentsetofdetectors“click”foreachBellstate.DistinguishingBellstates–cont.Aschemetomeasure2+Bellstates.Turnsoutthisisthebestwecandowithlinearelements.Non-lineardevicescanachieveacompletemeasurementbutwithlowefficiency.TeleportationAlicewantstosendaquantumbittoBob.Shecannotmeasurethestateandsendtheresults.Ifshesendsthequbititselfitmightdeteriorateonthewayortaketoomuchtimetogetthereifitisastateofamassiveobject.Teleportation–cont.Alicehasaphoton-qubitthatshewantstoteleport.Alicecreatestwoentangledphotons,2and3,andsendsphoton3toBob.SheperformsaBellmeasurementonphoton1andphoton2andsendsBobtheresult.Bobperformsatransformationofhisphoton3accordingtoAlice’sBellmeasurementresultandphoton3becomesareplicaofphoton1.Howdoesitwork?BeforeAlice’sBellmeasurementthecompletestateis: whichcanbeexpressedasByperformingaBellmeasurementonphotons1and2theymakephoton3collapseintooneoftheabovestates.BysendingtheresultAliceinstructsBobwhichtransformationtoperform–Paulimatrices.ExperimentallyAlicetakestwophotons(2,3)fromaPDCinananti-symmetricentangledstateandsendsphoton3toBob.Alicecreatesphoton1at45degrees,measuresonlyonphotons1and2andindicatestoBobaboutit.Inthisconfiguration,Bob’sphotonisimmediatelyareplicaofphoton1.Photon1isdestroyedinaccordancewiththeno-cloningtheorem.TeleportationwithcompleteBSMTeleportationwithcompleteBSMVerylowefficiency…DenseCodingBymanipulatingonephoton entangledinaBellstatewecan convertittoanotherBellstate.Manipulationofonephoton=fourBellstates=twobits!Wecanmeasure2+“1”outoffourBellstates.A“trit”:enhancementofthechannelcapacityby afactorofDenseCodingExperimentPhys.Rev.Lett.76,4656–4659

EntanglementSwappingMakingphotonsthathaveneverinteractedentangleusingmediators.Wewanttoentanglephotons1and4.Weentanglephotons1with2and3with4.Thecompletestateis:Now,performingaBellmeasurementonphotons2+3resultsinentanglementof1+4intothesamestateas2+3.OREntanglementSwappingExperimentEntanglementPurification-MotivationDistributionofentangledstatesbetweendistantlocationsisessentialforquantumcommunicationoverlargedistances.Thequalityofentangledstatesgenerallydecreasesexponentiallywiththechannellength.Errorcorrectioninquantumcomputation.EntanglementpurificationTakeonly“fourmode”casesNature

423,417-422(22May2003)QuantumRepeatersClassicalrepeaters:dividethechannelintoNsegmentsandenhancethesignalateachnode.Qubitscannotbeclonedateachnodeandre-sent.Quantumrepeaters:Ateleportationschemeinvolvingentanglementswappingandpurification.Worksinlogarithmictimeandpolynomialinresourceswithrespecttothechannellength.TheSchemeDividethechannelbetweenAandBintoNsegmentsbyN-1nodes:CreateanEPRpairoffidelitybetweeneverytwoadjacentnodes.Example:AteveryNodeperformaBellmeasurementofonephotononbothsides.Purifytheentang