量子首张量子纠缠图像

粒子物理中的量子纠缠与量子信息Quantumentanglementandquantuminformationinparticlephysics施郁复旦大学物理系第十届全国粒子物理会议,南京,2008.
4.
28.
合作者:吴岳良教授(中科院理论所)参考文献:YS,Phys.
Lett.
B641,75(06).
YSandY.
L.
Wu,arXiv:0712.
2288;EPJC(inpress).
IntroductionQuantuminformation(informationprocessingbasedonquantumresources,especiallyquantumentanglement)hasbeendiscussedinalmostallareasreignedbyquantummechanics,probablywiththeexceptionofparticlephysics.
Therehavebeenrelatedresearches,e.
g.
Bellinequalitiesinparticlephysics.
QIasafundamentalconceptQuantumInformationisnotjustuseful.
Asafundamentalconcept,itshouldbeconnectedtoparticlephysicsandrelativisticquantumfieldtheory,whichistheonlyconsistentcombinationofQMandspecialrelativity.
Inthistalk,wewilldescribeanattemptinthisdirection.
Highenergyquantumteleportationusingneutralkaons.
AneutralKaonasatwo-statesystemPseudoscalarswithJP=0.
C|K0i=|K0i,C|K0i=|K0i.
CP|K0i=|K0i,CP|K0i=|K0i.
CPeigenstates:|K1i=1√2(|K0i+|K0i),withCP=1;|K2i=1√2(|K0i|K0i),withCP=1.
P|K0i=|K0i,P|K0i=|K0i.
I3|K0i=12|K0i,I3|K0i=12|K0i.
S|K0i=|K0i,S|K0i=|K0i.
Mass(weakinteraction)eigenstatesEigenvalues:λS=mSiΓS/2andλL=mLiΓL/2.
"S',"L':shortandlonglifetimesofweakdecays1/ΓSand1/ΓL.
|KSi=1√1+||2(|K1i+|K2i)=1√|p|2+|q|2(p|K0i+q|K0i)|KLi=1√1+||2(|K2i+|K1i)=1√|p|2+|q|2(p|K0iq|K0i)τ:propertime.
~=c=1.
≈103characterizesCPviolation,p=1+,q=1.
Forourpurpose,≈0.
|KS(τ)i=eiλSτ|KSiKL(τ)=eiλLτKL|i|iLifetimesdiersignicantly:1/ΓS≈0.
8953*1010s,1/ΓL≈5.
114*108smLmS≈3.
483*1012MeVisnegligible,asmL≈mS≈497.
648MeV.
TwodimensionalHilbertspaceK0K0K1K2KSKLEPRentangledstateofneutralkaonsGeneratedfromthestrongdecayofvectormeson,whichcanbecreatedinee+annihilationat1GeV;orfrompp-annihilationatrest.
SimilarforneutralBmesons,fromUpsilon(4S)resonance,generatedinee+annihilationat10GeV.
φ|Ψi=1√2(|K0i|K0i|K0i|K0i).
JPC=1WhyentangledTheymustsatisfybosestatisticsunderexchange.
Exchange:Ccombineswithcoordinatepermutation.
ThusC=-1impliesantisymmetryundercoordinatepermutation.
(1)lFirstnotedbyLeeandYangin1960.
PreviousworksonentangledkaonsAlotofdiscussionshavebeenmadeonusingentanglekaonstotestQMagainstlocalhiddenvariablemodels(Belltheorem).
ItwasclaimedthatthissystemmayclosethelocalityloopholeanddetectionloopholeintestingBelltheorem.
ExperimentalconfirmationsofEPRcorrelation(1)producedinpp-annihilationintheCPLEARdetectorinCERN(1998).
K0K0PLB42,339(98)ExperimentalconfirmationsofEPRcorrelation(2)producedindecayintheKLOEdetectorin(2003,2006)K0K0DAΦNEφhep-ex/0312032;PLB642,315(06)ExperimentalconfirmationsofEPRcorrelation(3)producedinee+annihilationintheBELLEdetectorinKEKB(2004,2007).
B0B0J.
Mod.
Opt.
51,991(04);PRL99,131802(07)IntroductiontoteleportationAliceandBobshareanEPRpairaandb.
Alicealsoholdsanotherqubitcinacertainstate.
AlicemakesBellmeasurementonqubitsaandc.
(projectiononBellbasis).
DependingonAlice'sresult,Bobperformoneoffourunitarytransformationonhisqubitb,thusobtaintheoriginalstateofc.
Teleportation(continued)|Ψiab=1√2(↑a↓b↓a↑b)|Ψic=α↑c+ρ↓c.
|Ψicab=12|Φ+ica(α↓bρ↑b)+12|Φica(α↓b+ρ↑b)12|Ψ+ica(α↑bρ↓b)12|Ψica(α↑b+ρ|w2↓b),|Ψ+i=1√2(↑a↓b+↓a↑b)|Ψi=1√2(↑a↓b↓a↑b)|Φ+i=1√2(↑a↑b+↓a↓b)|Φi=1√2(↑a↑b↓a↓b)TeleportationusingneutralkaonsGenerationofanEPRpairAtt=0,aandbiscreatedasDecayunderweakinteraction:|Ψab(t)i=M(t)|Ψiab,M(t)=exp[i(λS+λL)Λbt],Λb=1/p1v2b|Ψab(0)i=1√2(|K0ia|K0ib|K0ia|K0ib)=1√2(|K2i|K1i|K1i|K2i)=r√2(|KLia|KSib|KSia|KLib),r=(|p|2+|q|2)/2pq=(1+||2)/(12)ThethirdkoanAthirdkoancisgeneratedatinanunknownstateNaturallydecays|Ψc(t)i=F(t)|K0ic+G(t)|K0ic,|Ψc(tz)i=α|K0ic+β|K0ic.
tzF(t)=[(α+βp/q)eiλSΛc(ttz)+(αβp/q)eiλLΛc(ttz)]/2,G(t)=[(αq/p+β)eiλSΛc(ttz)(αq/pβ)eiλLΛc(ttz)]/2.
Letcandacollide!
Spacetimediagram:EigenstatesofP,SandIofc+aP,S,Iareconservedbystronginteraction,whichgovernsc-acollision.
|φ1ica=|K0K0iwithP=1,S=2,I=1;|φ2ica=|K0K0iwithP=1,S=2,I=1;|φ3ica=|Ψ+i=1√2(|K0i|K0i+|K0ic|K0i),withP=1,S=0,I=1;|φ4ica=|Ψi=1√2(|K0i|K0i|K0ic|K0iwithP=1,S=0,I=0.
Three-kaonstatebeforecollision,decomposedinthestronginteractionbasis|Ψcab(t)i=|Ψc(t)i|Ψab(t)i=M(t)2{√2F(t)|φ1ica|K0ib√2G(t)|φ2ica|K0ib|φ3ica[F(t)|K0ibG(t)|K0ib]|φ4ica[F(t)|K0ib+G(t)|K0ib]}.
ItisnotaBellbasis.
Thisbasisisphysical,whileBellbasisisnot.
CollisionThecollisioneffectsaunitarytransformationinanegligibletimeintervalAsSisgovernedbystronginteraction,S|φiica(i=1,2,3,4)isstillaneigenstateofS,PandI,withthesameeigenvaluesasfor|φiica.
|Ψcab(tx)i=M(tx)2{√2F(tx)S|φ1ica|K0ib√2G(tx)S|φ2ica|K0ibS|φ3ica[F(tx)|K0ibG(tx)|K0ib]S|φ4ica[F(tx)|K0ib+G(tx)|K0ib]}.
SDetectionofoutgoingparticlesofc-acollisionUsingstronginteractionwithnuclearmatter,thedetectioncompletesAlice'stwo-particleprojectioninthebasis.
Probabilities:Correspondingprojectedstateofb:Decayaffectstheprobabilities.
|M(tx)|2|F(tx)|2/2,|M(tx)|2|G(tx)|2/2,|M(tx)|2[|F(tx)|2+|G(tx)|2]/4,|M(tx)|2[|F(tx)|2+|G(tx)|2]/4.
|K0ib,|K0ib,[F(tx)|K0ibG(tx)|K0ib]/p|F(tx)|2+|G(tx)|2,[F(tx)|K0ib+G(tx)|K0ib]/p|F(tx)|2+|G(tx)|2.
{S|φiica}AdoptastochasticstrategyThisisbecauseitishardtoimplementsubsequentunitarytransformationonb.
Bobchoosestoretainorabandonbparticle,basedontheprojectionresultofc-a.
Teleportationofismadeifprojectionresultofc-aisS|Ψica.
F(tx)|K0ib+G(tx)|K0ibVerificationscheme(1)DifferentprojectionresultsleadtodifferentvaluesofstrangenessratioNoprojection/teleportation:Successfulteleportation:verydifferentfrom1ξ(t)=1.
For|Ψ(t)ib=f(t)|K0ib+g(t)|K0ib,ξ(t)=|f(t)|2/g(t)|2.
ξ.
ξ(t)=|F(tx)(eΓSτ/2+eΓLτ/2)+G(tx)(eΓSτ/2eΓLτ/2)|2|F(tx)(eΓSτ/2eΓLτ/2)+G(tx)(eΓSτ/2+eΓLτ/2)|2,τ=Λb(ttx0).
ActualwayofobtainingstrangenessratioRepeatmanyrunsoftheprocedure.
Noprojection():allrunsareconsidered.
Teleportedstate:onlyconsiderthoserunsinwhichc-aareprojectedto"Manyrunsoftheprocedure"canbedonesimultaneouslyinabeamofparticles,sorealizedbydifferentevents.
ξ(t)=1S|Ψica.
Verificationscheme(2)DifferentprojectionresultsleadtodifferentvaluesofCPratio.
Noprojection/teleportation:Successfulteleportation:significantlydifferentfrom1.
Advantage1:validnomatterwhetherCPisviolated.
Advantage2:easyexperimentalimplementation,usingnon-leptonicdecays(CP=1:decayto2pions;CP=-1:decayto3pions).
ζ(t)=1.
For|Ψ(t)ib=u1(t)|K1ib+u2(t)|K2ib,ζ(t)=|u1(t)|2/u2(t)|2.
Anotherprocess:EntanglementswappingAandBareentangled,CandDareentangled.
AandCaresubjecttoameasurement(projection).
ThenBandDbecomeentangled,thoughtheynevermeet.
Entanglingpartnersareswapped.
Preparation|Ψdcab(t)i=M0(ttz)M(t)|Ψidc|Ψiab=M0(ttz)M(t)2(|Ψ+ica|Ψ+idb|Ψica|Ψidb|K0K0ica|K0K0idb|K0K0ica|K0K0idb).
Inadditionto|Ψiabgeneratedatt=0,anotherkaonpairdandcisgeneratedas|Ψidcattimetz.
|Ψdc(t)i=M0(ttz)|Ψidc,M0(ttz)=exp[i(λS+λL)Λd(ttz)].
CollisionSpacetimediagram:LetcandacollideattxDetectionCollision:Indetectingoutgoingparticlesfromthecollision,candaareprojectedto:S|Ψ+ica,S|Ψica,S|K0K0icaorS|K0K0ica.
Correspondinglydandbareprojectedto:|Ψ+ica,|Ψica,|K0K0icaand|K0K0ica,respectively,eachwithprobability|M0(txtz)M(tx)|2/4.
.
TheprojectionresultisrevealedbyP,SandIoftheoutcomesofcacollision,accordingtowhichbanddareretainedorabandoned.
|Ψdcab(tx+0)i=M0(txtz)M(tx)2(S|Ψ+ica|Ψ+idbS|Ψica|ΨidbS|K0K0ica|K0K0idbS|K0K0ica|K0K0idb).
Verificationscheme(1)MeasuretheSasymmetryofbanddManyrunsareneeded.
Noentanglementswapping(allrunsareconsidered):A(t)=0Entanglementswappingsucceeds(considerthoserunsinwhichc-aprojectto:A(t)=1A(t)=[pdiff(t)psame(t)]/[pdiff(t)+psame(t)]pdiff(t)(psame(t)):probabilitytohavedierent(same)strangenessvaluesS|ΨicaVerificationscheme(2)MeasuretheCPasymmetryofbanddManyruns(events)areneeded.
Noentanglementswapping(allrunsareconsidered):A(t)=-1Entanglementswappingsucceeds(considerthoserunsinwhichc-aprojectto:A(t)=1S|ΨicaA(t)=[pdiff(t)psame(t)]/[pdiff(t)+psame(t)]pdiff(t)(psame(t)):probabilitytohavedierent(same)valuesofCP.
SummaryTheneutralkaonwhosestateistobeteleportedcollideswithanEPRmember.
ThedetectionoftheoutgoingparticlesofthecollisioncompletestheprojectiontoaneigenstateofP,SandI,whichisconservedinthecollision.
ThisbasisisdifferentfromBellbasis,asusedintheoriginalteleportationscheme.
Conditionedontheprojection,teleportationcanbemadestochastically.
VerificationcanbemadebasedonstrangenessmeasurementsorCPmeasurements.
Thelatterisbetter.
Entanglementswappingcanalsobedone.
AnewfeatureInconventionalimplementationsofteleportation,itisonlythe"sole"(state),ratherthanthe"body"(matter),thatisteleported.
Butinparticlephysics,asdemonstratedinthepresentscheme,the"body"(particle)itselfbecomesakindof"sole"(stateofthequantumfield),andisteleported.
ConclusionQuantuminformationcanbediscussedinthesettingofparticlephysics.
LikethatQIstimulatesresearchesonquantumcoherenceinotherareas,similarworkscouldbedoneforparticlephysics.
Suchstudiescouldrevealsomenewfeaturesunavailableinnonrelativisticregime,anddeepconnectionsbetweenmatterandinformation,providenewinsightsonparticlephysics!
Thankyouforyourattention!