Experimental-Issues-in-Quantum-Measurement：在量子测量问题-22页PPT课件.ppt

1、Experimental Issues in Quantum MeasurementBeing a quantum physicist is like being an alcoholic.the first step is to admit you have a problem.Today,7.10.03:OVERVIEW a survey of some important situations in q.msmt.theory(“why bother coming to these lectures?”)13.10.03:SOME TECHNICAL BACKGROUND introdu

2、ction to“standard”quantum measurement theory (measurement postulate,collapse,von Neumann msmts,density matrices and entanglement,.)20.10.03:THE QUANTUM ERASER Bohr-Einstein debates Scully,Englert,Walther:complementarity vs uncertainty Two-photon experiments Alternate pictures(collapse vs correlation

3、s)27.10.03:OTHER MODERN EXPERIMENTS.FIRST TOPIC:InterruptionsMAKE THEM!Im going too fast.Im going too slow.You want to correct my grammar.You disagree with something I said.I seem to disagree with something Ive said.You have a question about something Ive said.You have a question about something com

4、pletely unrelated.VALID REASONS TO INTERRUPT ME:Some referencesI will not be following any particular textbook,but for obviousreasons,will draw disproportionately from experiments I myselfhave worked on.Appropriate references will be provide as the lectures progress.General references on quantum mec

5、hanics:Your favorite QM text+Shankars Principles of QMBackground on the quantum measurement problem:Wheeler&Zureks Quantum Theory and MeasurementBells Speakable and Unspeakable in Quantum MechanicsMy general perspective on these issues:References on my web page,physics.utoronto.ca/aephraim/aephraim.

6、htmlwhere slides from these lectures will be too,eventually“Speakable and Unspeakable,Past and Future”lanl.arxiv.org/abs/quant-ph/0302019The Copenhagen Viewpoint (Toronto description of)Bohr,Heisenberg:We must only discuss the outcomes of measurements.An experiment described to measure wave properti

7、eswill measure wave properties.An experiment described to measure particle propertieswill measure particle properties.In an experiment which measures wave properties,a questionabout particle properties is not a question about the outcome of real measurements it is“not a properquestion.”Wave and part

8、icle descriptions are“complementary”they cannever both be observed in a single experiment.The Bohr-Einstein debatesTwo-slit interference:the prototypical wavephenomenon.Each particle seems to“gothrough both slits”;we cantask which one it came from.Inserting“Welcher Weg”detectorsdestroys our ignoranc

9、e and thus the interference.“Heisenberg microscope”:photons which allow you to lookat the particle bounce off it,disturbing its momentum.M acintosh P IC Tim age form atis not supportedFeynmans Rules for interferenceIf two or more indistinguishable processes can lead to thesame final event(particle c

10、ould go through either slit andstill get to the same spot on the screen),then add their complexamplitudes and square,to find the probability:P=|A1+A2|2|eikL1+eikL2|2 1+cos k(L1-L2)If multiple distinguishable processes occur,find the realprobability of each,and then add:P=|A1|2+|A2|2|eikL1|2+|eikL2|2

11、 1 If there is any way even in principle to tell which processoccurred,then there can be no interference(if you knew which slit the particle came from,youd see a 1-slit pattern)!The quantum eraserspin-up()particlesWaveplate:flips the spin of particlespassing slit 2,without affectinglinear momentum.S

12、till no interference because we could check the spin ofthe particle,and discover which slit it had traversed.Must there be a disturbance?Bohr:Measurement of X disturbs P;et ceteraMeasurement means amplification of a quantum phenomenonby interaction with some“large”(classical)deviceMsmt involves some

13、 uncontrollable,irreversible disturbanceWe must treat the measuring device classically.Wigner:Why must we?What will happen to us if we dont?Scully,Englert,Walther:Complementarity is more fundamental than uncertainty.We can use information to destroy interference,without disturbing the momentum.Store

14、y,Tan,Collett,Walls:No.Any such measurement always disturbs the momentum.Wiseman(+Toronto experiment):Theyre both right.And we can measure how much the momentum is disturbed.RECALL:Spin-projections along different axes are“incompatible”(cant be measured simultaneously-like X&P)If you find Sz=+1(spin

15、),and then measure Sx,Sx=+1(spin)and Sx=1(spin)are equally likely.Then if you find one of those,and become equally likely.Bohr&Heisenberg tell us we must choose:we can know Sz,but give up all knowledge of Sx.or know Sx and give up all knowledge of Sz.The EPR“Paradox”and superluminal signalling?Parti

16、cle with 0 angularmomentum decays.here implies.here.but here implies.here.EPR:we could measure Sx on particle 1,but simultaneouslyknow what we would have undoubtedly gotten if we had measured Sz;arent these both real?Copenhagen:no wave function has both those properties defined and the wave function

17、 is all you can possibly know.EPR are cheating,discussing measurements they didnt do.Some important lessonsOne of the more subtle ones:You can extract very limited information from a single particle.In fact,to duplicate the particle,you must destroy it information in QM is never gained or lost.The f

18、irst one(only 30 years.or maybe 50,or 70+):QUANTUM MECHANICS IS NOT LOCAL(i.e.:it is not always possible to describe what happens inVienna without simultaneously taking into account whatis going on in Toronto even for times so short that evenat the speed of light,no signal could have connected the t

19、wo.)M a c in to s h P IC Tim a g e fo rm a tis n o t s u p p o rte dJohn BellM a c in to s h P IC Tim a g e fo rm a tis n o t s u p p o rte dM a c in to s h P IC Tim a g e fo rm a tis n o t s u p p o rte dM a c in to s h P IC Tim a g e fo rm a tis n o t s u p p o rte dNO CLONING!(.and yet,recent“qua

20、ntum cloning”experiments.)“Distinguishing the indistinguishable”Non-orthogonal quantum states cannot be distinguished with certainty.This is one of the central features of quantum information which leads to secure(eavesdrop-proof)communications.Crucial element:we must learn how to distinguish quantu

21、m states as well as possible-and we must know how well a potential eavesdropper could do.M a c in to s h P IC Tim a g e fo r m a tis n o t s u p p o r te dIf it gets through an H polarizer,.it could still have been 45,and its too late to tell.If it gets through a 45 polarizer,same story.BUT:a clever

22、 measurement can tell with certainty,25%of the time.BUT BUT:a non-standard quantum measurement can do better!A 14-path interferometer for arbitrary 2-qubit unitaries.Success!The correct state was identified 55%of the time-Much better than the 33%maximum for“standard measurements”(=everything in your

23、 textbook).I dont knowDefinitely 3Definitely 2Definitely 1Problem:Consider a collection of bombs so sensitive thata collision with any single particle(photon,electron,etc.)is guarranteed to trigger it.Suppose that certain of the bombs are defective,but differ in their behaviour in no way other than

24、thatthey will not blow up when triggered.Is there any way to identify the working bombs(orsome of them)without blowing them up?Quantum seeing in the dark(AKA:The Elitzur-Vaidman bomb experiment)A.Elitzur,and L.Vaidman,Found.Phys.23,987(1993)P.G.Kwiat,H.Weinfurter,and A.Zeilinger,Sci.Am.(Nov.,2019)BS

25、1BS2DCBomb absent:Only detector C firesBomb present:boom!1/2 C1/4 D1/4The bomb must be there.yetmy photon never interacted with it.Quantum CAT scansIf you measure momentum P.you dont know anything about X.If you measure position X.you dont know anything about P.But in real life,dont I know something

26、 about each?Dont I also know that if a car left this morning and is alreadyin Budapest,its going faster than if its still on Whringerstr.?Wigner function:W(x,p)is like the probability for a particle to beat x and have momentum p.Its integrals correctly predict P(x),P(p),and everything else you want.

27、Of course,you must study a large ensemble of particles to getso much information:“quantum state tomography”Macintosh PICTimage formatis not supportedmomentumpositionProbabilityP(0,0)(by measuring a particle to be in that state;see 4)Let Schrdinger do his magic:|i|f=U(t)|i,deterministicallyUpon a mea

28、surement,|f some result|n,randomly1.Forget|i,and return to step 2,starting with|n as new state.Aharonovs objection(as I read it):No one has ever seen any evidence for step 3 as a real process;we dont even know how to define a measurement.Step 2 is time-reversible,like classical mechanics.Why must I

29、describe the particle,between two measurements(1&4)based on the result of the first,propagated forward,rather than on that of the latter,propagated backward?Predicting the past.A+BWhat are the odds that the particlewas in a given box(e.g.,box B)?B+CA+BPick a box,any box.A+B+CA+BCWell see that applyi

30、ng similar logic here lets us conclude:P(A)=100%P(B)=100%and then,necessarily:P(C)=100%(?!).and that real measurements agree(somehow!)special|i a|0+b|1+c|2a|0+b|1 c|2Measurement as a tool:KLM.INPUT STATEANCILLATRIGGER(postselection)OUTPUT STATEparticular|f Knill,Laflamme,Milburn Nature 409,46,(2019)

31、;and others since.Experiments by Franson et al.,White et al.,Zeilinger et al.MAGIC MIRROR:Acts differently if there are 2 photons or only 1.In other words,can be a“transistor,”or“switch,”or“quantum logic gate”.Summary:the kinds of thingswell cover.Why does one thing happen and not another?When is a quantum measurement?Does a measurement necessarily disturb the system,and how?What can we say about an observable before we measure it?Does a wave function describe a single particle,or only an ensemble?Is a wave function a complete description of a single particle?Can we predict the past?22谢谢！谢谢！