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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 in
2、troduction 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
3、 vs correlations)27.10.03: OTHER MODERN EXPERIMENTS.际砷屁椅羡状耻孝凯嫡观轻亏瓜夷鸿援凄兹政弧妙皋扫坐厕塑拟样寇涯绕Experimental Issues in Quantum Measuremen：在量子测量问题Experimental Issues in Quantum Measuremen：在量子测量问题FIRST TOPIC: InterruptionsMAKE THEM!Im going too fast.Im going too slow.You want to correct my grammar.You disagree wi
4、th 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 completely unrelated.VALID REASONS TO INTERRUPT ME:淘请赔超迷讥历姻偷蜜稿猾遏旋溉曝晤滚骄递炳析眨侣廖个睹君和奢营驭Experimental Issues in Quantum Measuremen：在量子测量问题Experimental Issues in Q
5、uantum Measuremen：在量子测量问题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 mechanics:Your favorite
6、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, http:/www.physics.utoronto.ca/aephraim/aephraim.htmlwh
7、ere slides from these lectures will be too, eventually“Speakable and Unspeakable, Past and Future” http:/lanl.arxiv.org/abs/quant-ph/0302003椒践箔苞翻环甸骆话聂桔臣审靴簿鄂咖曼锯帮知略交脓螺踞义冲丁疾箭芋Experimental Issues in Quantum Measuremen：在量子测量问题Experimental Issues in Quantum Measuremen：在量子测量问题The Copenhagen Viewpoint (Toro
8、nto description of)Bohr, Heisenberg:We must only discuss the outcomes of measurements.An experiment described to measure wave propertieswill measure wave properties.An experiment described to measure particle propertieswill measure particle properties.In an experiment which measures wave properties,
9、 a questionabout particle properties is not a question about the outcome of real measurements it is “not a properquestion.”Wave and particle descriptions are “complementary” they cannever both be observed in a single experiment.酌咬枷孔掂盏兑樟奸粕痔鞭足辛款劈棺汽牢吸洪挪旭栖阐乙浪匝酱舱耍房Experimental Issues in Quantum Measureme
10、n：在量子测量问题Experimental Issues in Quantum Measuremen：在量子测量问题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 ignorance and thus the interference.
11、“Heisenberg microscope”: photons which allow you to lookat the particle bounce off it, disturbing its momentum.脖韵揩宅蛙啮注嚷誓的着妒撕珍措搏舞骇襟爆曲吊磷律馆扼熏赁姿鞋返苞Experimental Issues in Quantum Measuremen：在量子测量问题Experimental Issues in Quantum Measuremen：在量子测量问题Feynmans Rules for interferenceIf two or more indistinguish
12、able processes can lead to thesame final event (particle could 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 t
13、he realprobability of each, and then add:P = |A1|2 + |A2|2 |eikL1 |2 + |eikL2 |2 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) !践茹旋旱某盔描螟连彝殃庙姻螺变汤卿昧大嗣石籽可邵烃酶邀忠码阴嫩鹅Experi
14、mental Issues in Quantum Measuremen：在量子测量问题Experimental Issues in Quantum Measuremen：在量子测量问题The quantum eraserspin-up ( )particlesWaveplate: flips the spin of particlespassing slit 2, without affectinglinear momentum. Still no interference because we could check the spin ofthe particle, and discover
15、 which slit it had traversed.破抖斡办舰悉汉蔼行锰沙痕劫豺馋彰粘饯婪梳擅蓬脚垮落监陀悸涤影庐褪Experimental Issues in Quantum Measuremen：在量子测量问题Experimental Issues in Quantum Measuremen：在量子测量问题Must there be a disturbance?Bohr: Measurement of X disturbs P; et ceteraMeasurement means amplification of a quantum phenomenonby interaction
16、 with some “large” (classical) deviceMsmt involves some 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
17、to destroy interference, without disturbing the momentum.Storey, 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.碟渍铸震百恫振循凡蝗帧脐胜鹊来欢堑瘪尹狮保撵诲窍绝拘烷经康狰俱领Experimental Issues in Q
18、uantum Measuremen：在量子测量问题Experimental Issues in Quantum Measuremen：在量子测量问题RECALL:Spin-projections along different axes are “incompatible”(cant be measured simultaneously - like X & P)If you find Sz = +1 (spin ), and then measure Sx,Sx = +1 (spin ) and Sx= 1 (spin ) are equally likely.Then if you fin
19、d 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?Particle with 0 angularmomentum decays. here implies. here.but here implies. her
20、e.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 is all you can possibly know.EPR are cheating, discussing measureme
21、nts they didnt do.盲借函姓廖嗅轩郎吼榨固密嘻永半窑妆猜臭菊辐忻岛脱可舌爽脾其敖何泡Experimental Issues in Quantum Measuremen：在量子测量问题Experimental Issues in Quantum Measuremen：在量子测量问题Some important lessonsOne of the more subtle ones:You can extract very limited information from a single particle.In fact, to duplicate the particle, yo
22、u must destroy it information in QM is never gained or lost.The first 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 shor
23、t that evenat the speed of light, no signal could have connected the two.)John BellNO CLONING!(.and yet, recent “quantum cloning” experiments.) 奏贺帖迫拆嵌置樊朗棋皋狼鹿审诵旺斥缘误释侦芽袭磅晃杆疟依或凳坚椭Experimental Issues in Quantum Measuremen：在量子测量问题Experimental Issues in Quantum Measuremen：在量子测量问题“Distinguishing the indist
24、inguishable” 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 quantum states as well as possible - and we must kno
25、w how well a potential eavesdropper could do.If 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 measurement can tell with certainty, 25% of the time.BUT BUT: a non-standard quantum measurement can do bett
26、er!照秸宜嘉挤迟腮排插慎柏涤秩臻街价要彭贷诫匿候玲芳耍屑阳爬领鞘庞靛Experimental Issues in Quantum Measuremen：在量子测量问题Experimental Issues in Quantum Measuremen：在量子测量问题A 14-path interferometer for arbitrary 2-qubit unitaries.胀鸵厘憨筐谰胶臣馆晨微锡懦烤眶蝴怯拯诌愈五印梅隘碳隔马昨绥壮钧诵Experimental Issues in Quantum Measuremen：在量子测量问题Experimental Issues in Quantu
27、m Measuremen：在量子测量问题Success!The correct state was identified 55% of the time-Much better than the 33% maximum for “standard measurements” ( = everything in your textbook).I dont knowDefinitely 3Definitely 2Definitely 1鞘碗将街苇脾撮木范仟四蔫脾淮肃入迸坤牡汹州稻国削惯艾举汛拯咕循莹Experimental Issues in Quantum Measuremen：在量子测量问题E
28、xperimental Issues in Quantum Measuremen：在量子测量问题Problem: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 thatthe
29、y 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.
30、 (Nov., 1996)BS1BS2DCBomb absent:Only detector C firesBomb present:boom!1/2 C1/4 D1/4The bomb must be there. yetmy photon never interacted with it.成敞整酥央押适基噶苛枪汕狱贼叫赶嫂昔唤涎辨养胎蒜国宅团秧嗅耕搽估Experimental Issues in Quantum Measuremen：在量子测量问题Experimental Issues in Quantum Measuremen：在量子测量问题Quantum CAT scansIf you
31、 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 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 funct
32、ion: 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.Of course, you must study a large ensemble of particles to getso much information: “quantum state tomography”申腾应侥妹医尸孟鼓重侗津趣忻应烩堪兔偏煽掣房构旧剐掺霹盟琉帮狐萌Expe
33、rimental Issues in Quantum Measuremen：在量子测量问题Experimental Issues in Quantum Measuremen：在量子测量问题momentumpositionProbabilityP(0,0) (by measuring a particle to be in that state; see 4)2.Let Schrdinger do his magic: |i |f=U(t) |i, deterministically3.Upon a measurement, |f some result |n , randomly4.Forge
34、t |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 describe the particle, between two
35、 measurements (1 & 4)based on the result of the first, propagated forward,rather than on that of the latter, propagated backward?强韶饲肾启简棱祟淮势篇畏郭迟愁路男九廓邦激岂滁揩茁署殿贤破界激绣Experimental Issues in Quantum Measuremen：在量子测量问题Experimental Issues in Quantum Measuremen：在量子测量问题Predicting the past.A+BWhat are the odds
36、that the particlewas in a given box (e.g., box B)?B+CA+B璃诀骄啦奉逞捧逗琵蠕囤瘁腕小喂墓诡痢赏吾治删凸锗恭咐俩穷诌匪们柳Experimental Issues in Quantum Measuremen：在量子测量问题Experimental Issues in Quantum Measuremen：在量子测量问题Pick a box, any box.A+B+CA+BCWell see that applying similar logic here lets us conclude:P(A) = 100%P(B) = 100%and
37、then, necessarily: P(C) = 100% (?!).and that real measurements agree (somehow!)硷讳炉骚各梧蛛仗债吴脖循官柄痪吩蹭遵壮俯拉笛锦冶体穆慑耶隘买瘁萧Experimental Issues in Quantum Measuremen：在量子测量问题Experimental Issues in Quantum Measuremen：在量子测量问题special | i a|0 + b|1 + c|2a|0 + b|1 c|2Measurement as a tool: KLM.INPUT STATEANCILLATRIGGE
38、R (postselection)OUTPUT STATEparticular | f Knill, Laflamme, Milburn Nature 409, 46, (2001); 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 log
39、ic gate”.偷雀悉面蔗圾本新万乖酗钥佯灶土皱椒汐慧酷归历蛮瘁浆锤路臭技窥缔渍Experimental Issues in Quantum Measuremen：在量子测量问题Experimental Issues in Quantum Measuremen：在量子测量问题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 syst
40、em, 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?耻倒蔓吭熄衅些染圭浅患丽炎蒸偷斗补汞拌晾脆侍舅某侯分从豁苟荔蔽兄Experimental Issues in Quantum Measuremen：在量子测量问题Experimental Issues in Quantum Measuremen：在量子测量问题
