Quantum Erasure

In quantum mechanics, there are two sides to every story, but only one can be seen at a time. Experiments show that “erasing” one allows the other to appear

Stephen P. Walborn, Marcelo O. Terra Cunha, Sebastião Pádua and Carlos H. Monken

n 1801, an English gentleman scholar With his “slip of card,” Young set off Recently, physicists have started to Inamed Thomas Young performed a revolution in physics whose ripples shed some light on this mystery through one of the most celebrated experiments are still being felt today. His experi- the demonstration of quantum erasers— in the history of physics. Here is how ment is now a staple of freshman in which one can actually choose to turn he described it two years later, in a lec- physics laboratories, though it is now the interference fringes on or off. Our ture for the Royal Society of London: typically performed with two slits group has constructed a quantum eraser etched into a piece of opaque micro- using a more elaborate version of I made a small hole in a window film. (Thus the name, “Young’s double- Young’s experiment and used it to shutter, and covered it with a slit experiment.”) The phenomenon he demonstrate, in principle, the idea of thick piece of paper, which I per- had observed, called interference, can be “delayed choice,” in which the experi- forated with a fine needle.… I demonstrated easily enough with menter can make the decision after the brought into the sunbeam a slip of waves in a tank of water. Thus, by particle has been detected. The delayed- card, about one thirtieth of an inch analogy, Young’s experiment seemed choice experiment almost sounds like al- in breadth, and observed its shad- to prove that light is made up of tering the past. Lest any readers get ideas ow, either on the wall, or on other waves, as Dutch physicist Christiaan of building a “wayback machine,” we cards held at different distances. Huygens had advocated. But that was will explain why quantum erasers don’t What Young saw on the opposite not the end of the story. really change history. But we do believe wall was not, as one might guess, a In the early 1900s, physicists discov- that they clarify how interference phe- single thin shadow, but instead a ered that light does behave in some nomena arise in quantum mechanics. whole row of equally spaced light and ways as if composed of particles. In dark stripes or fringes, with the central particular, there is a smallest “quan- The Quantum Coin Toss band always bright. When he blocked tum” of light, called a photon. In 1909, The appearance of interference fringes the light on one side of the card, the Cambridge physicist Geoffrey Taylor in the classical double-slit experiment fringes went away. He concluded that repeated an experiment similar to is well understood. According to the light from both sides of the card was Young’s, which showed that individ- wave theory of light, when two beams required to make the pattern. But how ual photons suffer another interference of coherent light with the same wave- could two rays of light combine to phenomenon, called diffraction. By length encounter each other, they com- make a dark fringe? And why was the dimming the light until only one pho- bine. The most extreme situations are center of the shadow always bright, ton at a time reached the screen, he constructive interference, in which the instead of dark? This was hard to fath- eliminated any possibility that the pho- waves reinforce each other, or destruc- om if light was made of particles that tons could interfere with one other. Yet tive interference, in which they cancel traveled always in straight rays, an after recording the results of many each other out completely. idea that was shared by many physi- photons, Taylor found the same pat- In Young’s experiment, the paths cists, including Isaac Newton. tern of diffraction fringes. Apparently, from each slit to a given observation then, an individual photon could “in- point are not necessarily equal in terfere with itself.” length. When they are equal—that is, The authors perform research in quantum optics at And it wasn’t just photons. Other when the observation point is centrally the Universidade Federal de Minas Gerais (UFMG) objects that seemed indisputably “par- located between the slits—the waves in Belo Horizonte, Brazil. Stephen P. Walborn is ticle-like,” such as electrons, neutrons arrive in phase and interfere construc- nearing the end of his doctoral research in quantum and even molecules of carbon-60, the tively. That explains why Young al- optics. Marcelo O. Terra Cunha is a graduate student buckyball, have subsequently demon- ways saw a light band in the center of in physics and assistant professor of mathematics. Se- strated the same wavelike behavior. his card’s “shadow.” On either side of bastião Pádua and Carlos H. Monken are adjunct professors at UFMG and head researchers in the ex- The self-interference of individual par- this central band lies a region where perimental quantum optics group. Walborn’s ad- ticles is the greatest mystery in quan- one wave has to travel exactly half a dress: Departamento de Física, UFMG, Caixa Postal tum physics; in fact, Nobel Prize laure- wavelength farther than the other. 702, Belo Horizonte, MG 30123-970, Brazil. Inter- ate Richard Feynman pronounced it There the waves interfere destructively net: [email protected] “the only mystery” in quantum theory. and a dark band appears. Next comes © 2003 Sigma Xi, The Scientific Research Society. Reproduction 336 American Scientist, Volume 91 with permission only. Contact [email protected]. Figure 1. In a modern version of Thomas Young’s double-slit experiment, a helium-neon laser illuminates a piece of microfilm, into which two slits are etched 0.1 millimeter apart. Next, the laser beam passes through a divergent lens (center), which spreads it out so that the interference fringes produced by the double slits can be seen more readily on the screen at the back. Young’s 1801 experiment used much more humble equipment: sunlight, a pinhole to make the light coherent, a card to split the beam and no divergent lens. Even so, he was able to discern at least five bright bands on the far wall. (Photograph courtesy of the authors.) a region where one wave travels exact- 2, and we find, say, that 5 percent of the root of –1), not a positive real number. ly one wavelength farther than the oth- photons pass through slit 1 and trigger Thus two nonzero probability ampli- er. Here there is once again construc- the detector. So Prob (slit 1) = 5 percent. tudes (say, 0.1 + 0.2i and –0.1 – 0.2i) can tive interference and a band of light. Next we block slit 1 and find that 5 per- add to zero, which is never true of clas- To understand why quantum inter- cent of the photons pass through slit 2 sical probabilities. ference is unexpected, it may help to and trigger the detector: Prob (slit 2) = 5 Philosophically, the meaning of draw an analogy to a coin toss. If it is a percent. Now when we uncover both probability amplitudes is still a great fair coin, the probability of getting slits, creating two possible routes, we mystery. Clearly, though, a “quantum heads is 50 percent and the probability would expect to detect 10 percent of the coin” does not work the same way as a of getting tails is also 50 percent. The photons. But no! Because we placed the classical coin. Thanks to the superposi- probability of getting heads or tails is detector in a dark fringe, we can run tion principle, a photon, our “quantum the sum of the individual probabilities: the experiment for hours and not see a coin,” can give a combination of both single photon. That is, heads and tails. Prob (heads or tails) = Prob (heads) + Prob (tails) = 100 percent Prob (1 or 2) = 0 percent ≠ Matter Waves Matter Prob (1) + Prob (2) Now consider a quantum “coin toss” If all of this sounds pretty unbelievable based on Young’s experiment. We send The mind-bending explanation that to you, then you are in good company. a beam of light at the double-slit appa- quantum physicists have found for this Even the originators of quantum ratus, and put a photodetector a certain behavior is the principle of superposi- physics struggled with its concepts, distance away on the other side. To tion, which says that wavelike events and some of them never accepted the dramatize the paradox, we place it in combine according to a probability am- theories they were forced into. The the middle of a dark interference fringe. plitude rather than a probability. Math- German physicist Max Planck, who, in Now, we turn down the light so that ematically, a probability amplitude is a 1900, was the first to propose that light only one photon at a time passes complex number (that is, a number like behaved as if it were made up of quan- through the slits. First we cover up slit 0.1 + 0.2i, where i denotes the square ta, envisioned this only as some sort of © 2003 Sigma Xi, The Scientific Research Society. Reproduction www.americanscientist.org with permission only. Contact [email protected]. 2003 July–August 337 a constructive interference b constructive destructive

destructive interference

+ slits

screen

200 photons 6,000 photons

Figure 2. Physicists normally explain Young’s interference fringes with the wave theory of light (a). Two light waves reinforce each other constructively, creating a brighter beam when they are in phase, and reinforce each other destructively when they are out of phase (b). After light waves pass through the two slits, they will interfere constructively wherever one wave travels a whole number (0, 1, 2, …) of wavelengths farther than the other. They interfere destructively when one wave travels a fraction (1/2, 3/2, 5/2, …) of wavelengths farther. According to the geom- etry, this results in a series of equally spaced light and dark bands, called interference fringes (c). Modern versions of Young’s experiment make it possible to send one photon at a time through the slit apparatus. As this computer simulation shows, the interference pattern emerges unambiguously as the number of photons increases. Though none of the photons interfere with each other, somehow they continue to produce interference fringes. The only explanation seems to be that a photon can pass through both fringes simultaneously and interfere with itself. mathematical trick that happened to fit satisfaction that motivated and still ously, momentum is a wavelike ob- the experimental data. Unlike Planck, motivates much of the modern re- servable. In 1927, Louis de Broglie pro- Albert Einstein accepted the idea of search in quantum mechanics. posed that when a particle, such as an quanta of light, but had misgivings In the late 1920s, Danish physicist electron, acquires momentum it also over the later developments of quan- Niels Bohr formulated an interpreta- acquires a characteristic wavelength. tum theory. He could not come to tion of quantum mechanics known as According to Bohr, every quantum ob- terms with the idea that what we ob- the “Copenhagen interpretation” (see ject is both wave and particle, and the serve and consequently call “reality” “Science as Theater,” American Scientist, behavior we observe is determined seems to be random. (Quantum me- November–December 2002) that is the simply by the kind of measurement we chanics deals with probabilities and most widely accepted way of dodging choose to make. If we measure a parti- therefore does not say anything about the paradoxes of quantum physics. In cle-like property, then the object will where the photon is; only where it is particular, Bohr’s complementarity exhibit particle-like behavior. Later, if likely or unlikely to turn up.) Einstein principle states that for a pair of com- we choose to measure a wavelike prop- was bothered also by the implication plementary variables or “observables,” erty, we will see the object act as a that this reality exists in a unique, un- such as position and momentum, the wave. But we cannot do both at once. ambiguous state only when we are ob- precise knowledge of one prevents any On several occasions, Einstein serving. He expressed his discontent to knowledge of the other. Position is a thought he could poke holes in the Abraham Pais: “Do you believe that “particle-like” observable: A particle Copenhagen interpretation. One such the moon exists only when you look at has a specific location in space, but a criticism was a “thought experiment” it?” Interestingly, it was Einstein’s dis- wave does not. Somewhat less obvi- (never performed in a laboratory) in © 2003 Sigma Xi, The Scientific Research Society. Reproduction 338 American Scientist, Volume 91 with permission only. Contact [email protected]. which a double slit is suspended by best precision with which one can quantum erasure. Their logic was as sensitive springs so that it is free to measure complementary variables. follows: If the information providing move back and forth. When a photon The recoil of the double-slit apparatus the object’s trajectory can be deter- is scattered by the spring-loaded slits, it necessarily disturbs the system, and mined without significantly perturbing gives the apparatus a slight kick. By creates an uncertainty in the detection it, then the interference should disap- noting the recoil of the apparatus to- of the photon’s position on the detec- pear (in accordance with complemen- gether with the position at which the tion screen. This uncertainty is just tarity). But if that information is subse- photon is later detected, the experi- enough to blur the interference quently “erased,” then the interference menter could discover through which fringes, so that the momentum can no should return. One might even say that slit the photon “passed” (a position longer be measured. “interference equals ignorance” (of the measurement). At the same time, Ein- For many years it was thought that particle’s path). stein argued, the recoil measurement, Heisenberg’s principle was the mecha- Later, Scully joined with Berthold- made after the photon has passed, nism responsible for enforcing comple- Georg Englert and Herbert Walther, would not alter its trajectory, so the in- mentarity. However, it was recently hy- also of the Max Planck Institute, in terference fringes would still be ob- pothesized that complementarity is proposing a way to bring this about. In served. From the separation of the more fundamental—that it should be their proposal, the interfering object is fringes, the wavelength—a wavelike possible to “mark” a particle’s position an atom with electrons excited to a very property—could be inferred. Thus in a way that does not alter its momen- high energy level. Behind each of the both the momentum and the trajectory tum. This leads to a class of experi- slits is a microwave cavity designed to would be known, and the complemen- ments known as quantum erasers. capture a photon emitted by the atom tarity principle must be a hoax! as it decays to a less excited state. Sim- However, Bohr showed that Ein- Which Path? ply by looking to see which cavity con- stein’s argument had a flaw. To do so, Roughly 20 years ago, physicists Mar- tains the photon, the experimenter he invoked another principle of quan- lan O. Scully and Kai Drühl, then of the could tell which slit the atom passed tum mechanics: Heisenberg’s uncer- Max Planck Institute for Quantum Op- through. Complementarity implies that tainty principle. In spite of its vague- tics in Garching, Germany, and the the interference fringes would have to sounding name, this principle is a University of New Mexico, shook the disappear. But if the experimenter took very quantitative statement about the physics community with the idea of out the wall between the two cavities,

micromaser photon cavities detector

excited atoms

atoms

photon emitted by excited atom

detection screen laser

Figure 3. “Quantum eraser” thought experiment by Scully, Englert and Walther eliminates interference (a wavelike property) by recording information on which slit an excited atom went through (a particle-like property). An atom is excited to a high energy state by a laser. It then passes into the double-slit apparatus. Behind the slits are two microwave cavities that are sufficiently long for the atom to drop out of its excited state before it exits the cavity. This releases a photon, enabling the experimenter to detect which slit the atom passed through. According to Bohr’s complementarity principle, it cannot then act like a wave. Therefore, multiple repetitions of the experiment will produce a large blob on the detection screen instead of interference fringes. But removing the wall between the cavities would erase the “which-path” information, and interference would be restored. © 2003 Sigma Xi, The Scientific Research Society. Reproduction www.americanscientist.org with permission only. Contact [email protected]. 2003 July–August 339 like quantum coins but instead like boring, classical ones. The wave plates have now unambiguously correlated each slit with a particular polarization. Using a circular polarizer, we could measure the polarization and discover which slit each photon passed through. Note that we don’t actually have to measure the polarization to destroy the diagonally polarized wave interference pattern. It is enough that the which-path information is available 3 3 to us; playing dumb will not restore the interference.

2 An Entangled Story To demonstrate quantum erasure, one must do more than find a way to mark which path the photon took; one must also show how to “erase” that information. We do this by inserting a linear horizontal polarizer between the quarter-wave plates and the detector. When 1 11 we put the polarizer into place and re- a quarter-wave plate converts a diagonally polarized wave to a circularly polarized wave peat the experiment, instead of the bell-shaped curve of photon detec- Figure 4. Our version of quantum erasure uses polarization as a marker for which slit a photon tions, we see an interference pattern. passes through. A linearly polarized light wave (top) consists of alternating electric and mag- It’s as if we put on a pair of sunglasses netic fields. Here only the electric field is shown. Because it has equal horizontal and vertical and suddenly saw everything around components, it is said to be diagonally polarized (top, purple arrows). A quarter-wave plate, us in stripes. which the authors use in their experiments, retards one component (bottom figure). This caus- es the net electric field to rotate as it propagates through space (bottom, arrows 1, 2, 3, 4). Be- But how can that be? We have al- cause the rotation is counterclockwise to a viewer looking at the incoming wave, this is called ready said that simply playing dumb a left-circularly polarized wave. Retarding the other component would have created a right-cir- does not bring back interference. Why cularly polarized wave. With its axis vertical, the quarter-wave plate turns diagonally polarized does a horizontal polarizer bring it light into circularly polarized light, and with the axis at 45 degrees, it turns vertically polarized back? The answer is that it erases the light into circularly polarized light. which-path information. Remember that our horizontal polarizer filters ei- the extra “which-path” information the direction of polarization, or to ther a right-circular or left-circular po- would be erased, and—presto!—the change a linearly polarized beam into a larized photon into a horizontally po- fringes should reappear. circularly polarized one. Another com- larized one, so that there is no longer So far no one has succeeded in per- mon optical component is a polarizer, any way to tell the difference between forming the Scully-Englert-Walther ex- which allows only light with a given them. So once a photon has passed periment. However, we have performed polarization to pass. When a circularly through the polarizer, it cannot be de- an analogous experiment using photons, polarized beam passes through a hori- termined whether it came from slit 1 which is much easier to implement. zontal polarizer, the vertical part of the or slit 2. With the particle-like informa- Our experiment uses polarization as wave is stripped away and all that re- tion removed, the photons are free to a path marker. Any electromagnetic mains is a horizontally polarized beam, start acting like waves again. wave, such as light, has a polarization half as intense as the original. Similarly, if we place a linear vertical determined by the oscillations of the Now imagine that we repeat polarizer between the quarter-wave electric and magnetic fields that make Young’s experiment with many hori- plates and the detector, we again erase up the wave. (See Figure 4.) These fields zontally polarized photons. Behind the the which-path information. However, always oscillate in a plane perpendicu- slits we insert two quarter-wave plates, in this case we observe a fringe pattern lar to the direction of propagation, but one that turns the horizontally polar- —commonly called anti-fringes—that they can point in various directions ized photons into right-circularly po- is exactly out of phase with the pattern within this plane: for example, vertical- larized photons, and the other that we saw through the horizontal polariz- ly, horizontally, or at an angle of 45 de- makes them left-circularly polarized. er. Anti-fringes exhibit a central mini- grees or –45 degrees to the horizontal. Remarkably, the interference fringes mum (dark stripe). They can even rotate as they propagate will disappear and be replaced with a We now have two ways of dividing forward, so that the light wave turns single swath of light, most intense in the experimental results into subsets. like a right-handed screw or its mirror the middle. If we plot the distribution With a circular polarizer, we could image, a left-handed screw. Such of photons on a graph we get a bell- separate the photons into two groups: waves are said to be (right- or left-) cir- shaped curve. those that passed through slit 1 (right- cularly polarized. Optical components What happened to the interference? circular) and those that passed called wave plates can be used to change The photons no longer seem to behave through slit 2 (left-circular). With a © 2003 Sigma Xi, The Scientific Research Society. Reproduction 340 American Scientist, Volume 91 with permission only. Contact [email protected]. linear polarizer, we can separate them tangled with the path. The photon’s Telepathic coins may seem pretty into two different groups: those that state can be described as a new and weird. They did to Einstein, too; in a give a fringe pattern (horizontal) and more complicated superposition: famous 1935 paper with Boris Podol- those that give an antifringe pattern sky and Nathan Rosen, he argued that (slit 1 AND right-polarized) + (vertical). This is the essence of quan- they would violate the complementar- (slit 2 AND left-polarized) tum erasure. ity principle. Nevertheless, quantum Does the uncertainty principle say Because the two observables are entanglement is very much a reality. anything about this experiment? No. Po- now entangled, manipulating the in- Physicists are now experimenting, larization and position are not comple- formation about either one automati- both theoretically and in the laborato- mentary variables, so, as in the Scully- cally changes information about the ry, with ways to use entanglement in Englert-Walther proposal, Heisenberg’s other. It is completely equivalent to de- quantum computers and unbreakable uncertainty principle does not apply scribe the photon’s state as: cryptosystems. here. So what is enforcing the comple- (fringes AND horizontal-polarized) + mentarity principle? Changing History? (anti-fringes AND vertical-polarized) The answer is quantum entanglement. Our last variation on Young’s experi- When a photon passes through the To return to the coin-toss analogy, the ment incorporates quantum entangle- double-slit apparatus, it enters a superposition and polarization observables ment in a much more overt way, to position of position states: slit 1 + slit 2. are now like two “telepathic” coins. produce a seemingly paradoxical situ- The quarter-wave plates perform an Coin 1 lands heads half the time and so ation known as delayed choice, origi- additional conditional logic operation. does coin 2, so if you look at either one nally proposed by John A. Wheeler. If the photon passes through slit 1, it in isolation it appears completely nor- Even spookier than telepathic coins, emerges with right-circular polariza- mal. Their quantum strangeness only delayed choice seems to open up the tion and if it passes through slit 2, it emerges when you start flipping them, possibility of changing the past. But we emerges with left-circular polarization. and discover that every time coin 1 emphasize the word “seems”—in real- Thus the polarization has become en- lands heads, coin 2 does too! ity it does nothing of the sort.

quarter-wave plates provide “which-path” information

photon

double-slit and quarter-wave plates screen

horizontal polarizer erases “which-path” information

photon

double-slit and quarter-wave plates screen

Figure 5. In the authors’ version of quantum erasure, quarter-wave plates are placed behind the slits, converting the photons to left-circular and right-circular polarizations respectively. This makes “which-path” information available to the experimenter, and the interference fringes disappear (top). However, a horizontal polarizer (bottom) converts either of the circular polarizations to horizontal polarizations so there is now no longer any way to distinguish between photons that went through the top and bottom slits. “Which-path” information is erased, and—as the authors have demonstrated in the laboratory—the interference fringes return. © 2003 Sigma Xi, The Scientific Research Society. Reproduction www.americanscientist.org with permission only. Contact [email protected]. 2003 July–August 341 argon laser detector b UV laser beam

lens photon b (quantum eraser)

non linear coincidence counter crystal photon a

detector a entangled double-slit photons and quarter-wave plates

Figure 6. In “delayed-choice” experiment, a second photon is used as the quantum eraser. Photons a and b are prepared in an entangled state, so that any measurement of the polarization of b immediately determines the polarization of a. After photon a passes through the slit apparatus, the polarization of b is entangled with the “which-path” information for photon a. Coincidence detection allows the experimenter to de- termine which photons are entangled with one another. If both detectors light up within a nanosecond of each other, then the two photons are almost certainly an entangled pair.

In the delayed-choice experiment, tal” means it passed through slit 2.) To wave plates on Earth. Her friend Bob, we create a pair of entangled photons, erase the which-path information for a, who lives on Mars, sends her a box of which we will call a and b, in such a we can measure instead the diagonal photons. Alice sends each photon way that whenever photon a is ob- polarization of b. A measurement of through the double-slit apparatus and served to have horizontal polarization, the positive diagonal direction (45 de- then measures its position: “Photon photon b will necessarily be vertically grees) will give interference fringes on 567 was detected at position x = 4.3.” polarized, and vice versa. (We do this a’s detection screen, while a measure- Little does she know that Bob, on by a nonlinear optical process called ment in the negative diagonal direction Mars, has kept an entangled twin of “spontaneous parametric down-con- (–45 degrees) will produce anti-fringes. each photon. For each twin he chooses version,” in which we shine an ultravi- In our laboratory, we have demon- to measure the polarization, either in olet argon laser onto a thin crystal, strated that the quantum eraser effect the horizontal and vertical directions which emits two “twin” photons.) We occurs regardless of the order a and b or in the +45 degrees and –45 degrees maneuver photon a so that it passes are detected in. Because our detector diagonal directions. He writes the re- through the double slit and the quar- for photon b is not very far away (1.5 sults down in his lab book, “Photon ter-wave plates and then on to a detec- meters), the delay in detection between 567(B) was detected with horizontal tor, while b goes directly to a separate a and b is minuscule—about 5 nanosec- polarization.” A few weeks later, Bob polarization detector. This time the po- onds. But there is no reason in princi- pays Alice a visit. larization of photon b will be our quan- ple why we couldn’t send b very far Alice: Hi Bob! How’s Mars? Look, I tum eraser controller. away—say, out to Mars. This would did that double slit and quarter-wave Because a and b are entangled, any give the observer on Mars several min- plate experiment that those physicists measurement of b tells us something utes to decide whether we, back on wrote about. Just as they said, I got a about a. We can choose either to make Earth, will observe fringes or no boring bell-shaped curve, with no in- a measurement on b that provides fringes. But what if we have already terference at all. which-path information for a, or we collected our data and observed the Bob: (a prankster) Are you sure? Here, can make a measurement that pre- opposite thing? go back to your data and plot the posi- serves interference. If we measure the In fact, this cannot happen. The de- tions of just these photons. (He hands horizontal or vertical polarization of b, layed measurement on Mars doesn’t Alice a list of the photons for which he mea- we preserve the which-path informa- change any events on Earth—it only sured +45 degrees polarization.) tion. (This is true because, for example, changes our bookkeeping. Here is the Alice: Wow! Interference fringes! “a right-circular AND b horizontal” explanation, in the form of an imagi- How did you make the photons inter- means that photon a went through slit nary dialogue. Suppose Alice sets up a fere after they were already recorded 1, while “a left-circular AND b horizon- double-slit experiment with quarter- in my lab book? © 2003 Sigma Xi, The Scientific Research Society. Reproduction 342 American Scientist, Volume 91 with permission only. Contact [email protected]. total photon counts photon b photon a

peak one peak two horizontal right-circular (horizontal (vertical polarizer polarization polarization) polarization) slit 1 provide vertical left-circular polarizer polarization slit 2 measure horizontal or vertical “which-path” information “which-path” polarization of photon b preserves “which path”

positive diagonal interference polarizer fringes fringes anti-fringes (positive diagonal (negative diagonal polarization) polarization) erase negative interference diagonal anti-fringes polarizer “which-path” information “which-path” measure diagonal polarization to erase “which path”

Figure 7. “Delayed-choice” paradox (see Figure 6) amounts to a change in bookkeeping, not a change in history. The behavior of a pair of entangled photons (a and b) can be recorded independently by two observers. Observer A repeats the experiment many times and plots a graph showing where the photons are detected. Regardless of which kind of measurement observer B chooses, observer A’s graph will be a bell- shaped curve. (This corresponds to the “blob” seen in Figure 5.) If observer B chooses to measure horizontal/vertical polarization, each of his b photons will retain “which-path” information for their entangled twins. Thus the a photons that A has measured will separate into two groups, one that passed through slit 1 and one that passed through slit 2. The photon counts for each of these groups will produce bell-shaped curves, slightly displaced from one another (upper right, green lines). If observer B chooses to measure diagonal polarization, the “which-path” information will be erased. In that case, the entangled photons that A has measured can be separated into two different groups, one forming interference fringes and the other forming anti-fringes (bottom).

Bob: You think that’s cool? Check this Bob: Believe me Alice, somebody is Bibliography out. (Now he hands Alice a list of the photons already working on that. Feynman, R. P., R. B. Leighton and M. L. Sands. he measured with vertical polarization.) 1965. The Feynman Lectures on Physics. Read- Alice: No fringes! It’s back to a bell- Conclusion ing, Mass.: Addison-Wesley. shaped curve again. (Bob hands her a list Presumably, Einstein would not be Peres, A. 1995. Quantum Theory: Concepts and Methods. New York: Kluwer Academic Pub- of the photons with –45 degrees polariza- happy with these experiments. Quan- lishers. tion and she plots their positions.) Now tum erasure seems to confirm that the Scully, M. O., B. G. Englert and H. Walther. the interference is back, but this time complementarity principle is indeed a 1991. Quantum optical tests of complemen- anti-fringes. Bob, this is amazing. You fundamental part of quantum theory. tarity. Nature 351:111–116. have control over the past. Can you go Although such experiments have done Scully, M. O., and M. S. Zubairy. 1997. Quan- back and change my exam grades? much to illustrate the dual nature of tum Optics. New York: Cambridge Universi- Bob: I’m sorry, Alice, but there is no quantum objects, physicists are still un- ty Press. Walborn, S. P., M. O. Terra Cunha, S. Pádua magic here. The photons I gave you able to explain why wave-particle dual- and C. H. Monken. 2002. Double-slit quan- were actually entangled with photons I ity exists. In this respect, we would still tum eraser. Physical Review A 65:033818. kept for myself. I did polarization mea- agree with Richard Feynman, who Wheeler, J. A., and W. H. Zurek. 1983. Quantum surements on them, and that is where wrote in the 1960s, “We cannot make Theory and Measurement. Princeton Univer- these mysterious lists of photons came the mystery go away by explaining sity Press. from. But my measurements didn’t how it works. We will just tell you how change history. All they told me was it works.” how to divide up your experimental Even so, we are making progress. results. I can either divide them into We understand now that quantum en- fringes and anti-fringes, or I can divide tanglement, a necessary part of the act For relevant Web links, consult this issue of them into two bell-shaped curves. But I of measurement itself, rather than the American Scientist Online: can’t change where any individual “quantum uncertainty” involved in the photon actually landed. measurement, is responsible for com- http://www.americanscientist.org/ Alice: Rats. I really needed that A in plementarity in the double-slit experi- template/IssueTOC/issue/394 physics. (Brightens.) But hey! Maybe ment. This may seem like a subtle we can make this into a scheme for point, but it will make many physicists sending secret messages! sleep more soundly at night. © 2003 Sigma Xi, The Scientific Research Society. Reproduction www.americanscientist.org with permission only. Contact [email protected]. 2003 July–August 343