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CHAPTER 8
Beam Me a Bunny:
Quantum Teleportation
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Emmy trots into my office, looking pleased with herself. This is never a good sign.
“I have a plan!” she announces.
“Really. What sort of plan is this?”
“A plan to get those pesky squirrels.” They keep escaping up the trees in the garden, and she’s getting frustrated.
“Is this a better plan than the one where you were going to learn to fly by eating the spilled seed from the bird feeder?”
“That was going to work,” she says, indignantly. “And for your information, yes, it’s a much better plan than that.”
“Well, then, I’m all ears. What’s this brilliant plan?”
“Teleportation.” She looks smug, and wags her tail vigorously.
“Teleportation?”
“Yes.”
“Okay, you’re going to have to explain that a little.”
“Well, I’m thinking, the problem is, they can see me coming from the house, and they get to the trees before I do. If I could get between them and the trees, though, I could get them before they get away.”
“Okay, I’m with you so far.”
“So, I just need to teleport out into the garden, instead of going through the door.” Her whole back end is wagging now.
“Right … And how, exactly, did you plan to accomplish this feat?”
“Well … I was hoping you would help me.”
“Me?”
“Yes. I read where some physicists have done quantum teleportation, and you’re a physicist, and you’re really clever, and you know about quantum, so I was hoping you would help me build a teleporter.” She puts her head in my lap. “Pleeeeease? I’m a good dog.”
I scratch behind her ears. “You are a good dog, but I really can’t help. For one thing, I don’t do teleportation experiments in my lab. But even if I did, I wouldn’t be able to help you use teleportation to catch squirrels.”
“Why not?”
“Well, the existing teleportation experiments all deal with single particles, usually photons. You’re made up of probably 1026 atoms—a hundred trillion trillion—which is far more than anybody has ever teleported.”
“Yes, but you’re really clever. You can just … make it bigger.”
“I appreciate your confidence, but no. The bigger problem is that the quantum teleportation people do in the real world isn’t like the teleportation you see with the transporters on Star Trek.”
“How so?”
“Well, all that quantum teleportation does is transmit the state of a particle from one place to another. If I have an atom here, for example, I can ‘teleport’ it to the garden, and end up with an atom there that’s in the exact same quantum state as the atom I started with here. At the end of the process, though, I still have the original atom here where it started—it doesn’t move from one place to another.”
“That’s pretty rubbish. What’s the point of that?”
“Well, quantum mechanics won’t let you make an exact copy of a state without changing the original state, and quantum states of things like atoms are pretty fragile. If you really needed to get a particular quantum state from one place to another, your best bet might be to teleport it.” She looks a little dubious. “You could use it to make a quantum version of the Internet, if you had a couple of quantum computers that you needed to connect together.”
“Well, okay. So just teleport my state into the garden, and I’ll use it to catch squirrels.”
“Even if I knew how to entangle your state with a whole bunch of photons—which I don’t—I would need to have raw material out in the garden. There would need to be another dog out there, one that looked just like you.”
Her tail stops dead. “We don’t like those dogs,” she says. “Dogs that look just like me. In my garden. We don’t like those dogs at all.” She looks distressed.
“No, we don’t. One of you is all the dog we need.” She perks up a bit. “So, you see, teleportation isn’t a good plan, after all.”
“No, I suppose not.” She’s quiet for a moment, and looks thoughtful. “Well,” she says, “I suppose it’s back to plan A.”
“Plan A?”
“Can I have some birdseed?”
“Quantum teleportation” is probably the best-known application of the nonlocal correlations discussed in the previous chapter. The name certainly fires the imagination, conjuring up images of Star Trek and other fictional settings in which people, either through fictional science or just plain magic, can instantaneously transport objects from one place to another. The object starts at point A, disappears with a soft *whoosh*, and reappears at point B, some distance away.
The high expectations created by science fiction make the reality of quantum teleportation seem disappointing. Real quantum teleportation involves only the transfer of a quantum state from one location to another, and not the movement of complete objects. The transfer is also slower than the speed of light, because information needs to be sent from one place to another. This is a great disappointment to dogs hoping to beam themselves out into places where unsuspecting squirrels are waiting.
Nevertheless, it’s a marvelously clever use of quantum theory, tying together several of the topics that we’ve already talked about. In this chapter, we’ll see how indeterminacy and quantum measurement make it difficult to transmit information about quantum states from one place to another. We’ll see how the “quantum teleportation” scheme makes ingenious use of nonlocality and entangled states to avoid these problems, and why you might want to.
Quantum teleportation is a complex and subtle subject, probably the most difficult topic discussed in this book. It’s also the best example we have of the strangeness and power of quantum physics.
DUPLICATION AT A DISTANCE: CLASSICAL “TELEPORTATION”
We can’t teleport in the way envisioned in science fiction and fantasy, but the essence of teleportation is just duplication at a distance—you take an object at one place, and replace it with an exact copy at some other location. By that definition, we do have an approximation of teleportation using classical physics: a fax machine.
If you have a document that you want to send instantly from one place to another—for example, if Truman has just been given a really nice bone, and wants to taunt RD by sending him a picture of it—you can do this with a fax machine. The machine works by scanning the document, converting it to electronic instructions for creating an identical document, and sending that information over telephone lines to another fax machine at a distant location, which prints a copy. What’s transmitted is not the document itself, but rather information about how to make that document.
The operation of a fax machine is different from the fictional idea of teleportation, but the differences are not all that significant. When you fax a document from one place to another, you end up with two copies in different locations, but if you regard this as a problem, you could always attach a shredder to the sender’s fax machine to destroy the original. The copy produced by a fax machine isn’t perfect, but that’s just a matter of the resolution of the scanner and printer, and you can always imagine getting a better scanner and printer. The transmission is limited by the time it takes to transmit the information from one place to another, so it’s not perfectly instantaneous, but that’s not a major problem for most transactions involving a fax machine.
If you wanted to approximate the fictional ideal of teleportation in a classical world, the best you could do would be to upgrade the concept of the fax machine. Truman would take a bone, and place it in a machine, which would scan the bone to determine the arrangement of atoms and molecules making up the bone. Then he would send this information to RD’s “teleportation” machine, which would assemble an identical bone out of materials at hand and present it to him to chew.
NO CLONING ALLOWED: QUANTUM LIMITATIONS
When we turn to quantum teleportation, we’re talking about “teleporting” a quantum object. This means not just getting the right physical arrangement of the atoms and molecules making up the object, but also getting all those particles in the right quantum states, including superposition states. Truman could use an upgraded fax machine to send RD a cat in a box, but he would need a quantum teleportation device to send a cat in a box that was 30% alive, 30% dead, and 40% bloody furious. This turns out to be vastly more difficult than the classical analogue, due to the active nature of quantum measurement.
While in theory it is possible to do quantum teleportation with any object, in practice, all of the experiments done to date have used photons, so we’ll imagine that Truman is trying to send a single photon of a particular polarization to RD.* As we saw back in chapter 3 (page 65), a polarized photon can be thought of as a superposition of horizontal and vertical polarizations, with some probability of finding either of those two allowed states.
When we describe a photon with a polarization between vertical and horizontal, we write a wavefunction for that photon that is a superposition state: it’s a parts vertical, and b parts horizontal:
a |V> + b |H>
The numbers a and b tell us the probability of finding vertical or horizontal polarization.† In fact, any object in a superposition state will be described by a wavefunction exactly like this one. If we can find a way to teleport a photon polarization from Truman to RD, we can use the same technique to teleport the state of a cat in a box—it’s just a matter of increasing the number of particles involved.
So, Truman has a photon that he wants to send to RD. The classical recipe tells him to simply measure the polarization of the photon, then call RD on the phone, and tell him how to prepare an identical state. But the only way Truman can measure the polarization is if he already knows something about the state, and can set his polarization detector appropriately. For example, if he knows that the photon is either vertical or horizontal, he can send it at a vertically oriented polarizer. If it passes through, he knows that the polarization was vertical, and if it gets absorbed, he knows it was horizontal. He can then send that information to RD, who can prepare a photon in the appropriate state.
Unfortunately, if the polarization is at some intermediate angle—a parts vertical and b parts horizontal—it’s impossible for Truman to make the necessary measurement. The numbers a and b tell us the probability of the photon passing through a vertical or horizontal polarizer, but there’s no way of measuring both a and b for a single photon—either it passes through a polarizer or it doesn’t. Even if the photon passes through, the superposition is destroyed and it’s left in one of the allowed states.
You can only determine both probabilities by repeating the measurement many times using identically prepared photons. That doesn’t help us to transmit the polarization of a single photon, though, which is our goal.
This polarization measurement problem is a specific example of the no-cloning theorem. William Wootters and Wojchiech Zurek proved in 1982 that it is impossible to make a perfect copy of an unknown quantum state. Unless you already have some idea what the state is, you change the state when you try to measure it, and can never be sure that your copy is faithful. If Truman really needs to send RD a perfect copy of a single photon, without knowing its polarization in advance, he’ll need to find a more clever way of doing it.
“Why not just send the photon?”
“Pardon?”
“I mean, it’s a photon. They travel places at the speed of light—that’s what they do. If I had a photon and I wanted to send it to some other dog—which I don’t, by the way. Other dogs don’t deserve my photons. If I did, though, I would just point the photon at the other dog, and let it go.”
“Oh. Well, there are a lot of things that can happen to a photon on the way from one place to another that would change the polarization. If you want to be sure that the dog on the other end gets exactly the polarization you started with, teleportation is a sure way of doing that.”
“That’s a silly thing to want to do, anyway.”
“Not really, but you’ll have to wait until the end of the chapter to find out why.”
A MAGIC COMPASS: CLASSICAL ANALOGUE OF QUANTUM TELEPORTATION
It’s hard to find a classical analogue for quantum teleportation, because the issues involved are inherently nonclassical. But we can get a little of the flavor of what’s involved by thinking of the photon teleportation process in graphical terms. We can also get a hint of what quantum teleportation will really require.
As we saw in chapter 3 (page 66), we can represent a photon polarization by an arrow indicating the direction of polarization. We can think of the horizontal and vertical components in terms of the number of steps we take in the different directions: you take a steps in the vertical direction, and b steps in the horizontal direction.
In this graphical picture, teleportation is a problem of aligning arrows. Truman has an arrow pointing in some direction, and both dogs will get steak if RD can make his arrow point in the same direction. How do they manage this?
The only way the two dogs can get their arrows aligned is if they have some shared reference. If they each have a compass, Truman can compare his arrow to the direction of the compass needle, and tell RD to point his arrow, say, 17° east of due north. The compass provides a reference that they both share, and any scheme for photon teleportation will need a similar reference.
Representing light polarization as a sum of horizontal and vertical components. The larger arrows represent two different photon states, while the smaller arrows are the vertical and horizontal components.
The problem of teleporting a photon is much harder than simply aligning arrows, though, because of the no-cloning theorem. Truman can’t measure the direction of his arrow without disturbing it. Somehow, he needs to communicate the direction of his arrow to RD without measuring it. What he needs is a nonlocal reference, a kind of magic compass that can communicate a direction to RD’s compass without making a measurement. Quantum teleportation is possible because the quantum entanglement that we discussed in chapter 7 provides this kind of nonlocal reference.
BEAM ME A PHOTON: QUANTUM TELEPORTATION
Quantum teleportation was developed in 1993 by a team of physicists working at IBM (including William Wootters of the no-cloning theorem). It uses a four-step process to transfer an unknown state from one place to another:
FOUR STEPS FOR QUANTUM TELEPORTATION
1. Share a pair of entangled particles with your partner.
2. Make an “entangling measurement” between one of the entangled particles and the particle whose state you want to teleport.
3. Send the result of your measurement to your partner by classical means.
4. Tell your partner how to adjust the state of his particle according to the measurement result.
This recipe for teleportation exploits quantum entanglement to generate a copy of an arbitrary state at a distant location through one measurement and a phone call. It uses the active nature of quantum measurement to align one of the two entangled photons with the state to be “teleported.” In the process, the second entangled photon is instantly converted to a polarization that depends on the original state. The no-cloning theorem still applies, so the state of the original particle is altered by the measurement, but at the end of the process, the second entangled photon is in the same state as the original photon before “teleportation.”
Here’s how it works: let’s imagine that Truman has a single photon in a particular polarization state, and he wants to get exactly that state to his old friend RD (but he can’t just send it straight there). Anticipating that this situation might come up, Truman and RD have previously shared a pair of photons in an entangled state, each taking one. The polarizations of these photons are indeterminate until measured, but they are guaranteed to be opposite each other. So, the two dogs have a total of three photons: Photon 1 is the state that Truman wants to convey to RD (at some randomly chosen angle, described by a|V> + b|H>), Photon 2 is Truman’s photon from the entangled pair, and Photon 3 is RD’s photon from the entangled pair. The teleportation procedure outlined above will allow RD to turn his Photon 3 into an exact copy of Photon 1.
A cartoon version of quantum teleportation. At the beginning of the process, Truman has two photons, Photon 1 in a definite (though unknown) state that he wants to send to RD, and Photon 2 in an indeterminate state that is entangled with RD’s Photon 3. After the teleportation procedure is completed, Truman has two photons in an indeterminate state entangled with each other, and RD has a photon whose polarization is identical to the original polarization of Photon 1.
Teleportation works because quantum physics is nonlocal. We saw in chapter 7 that any measurement Truman makes on Photon 2 will instantaneously determine the polarization of RD’s Photon 3. Of course, it’s not as simple as measuring the individual polarizations of Photon 1 and Photon 2—we already saw that that won’t work. Instead, what Truman does is to make a joint measurement of the two photons together. He measures whether the two polarizations are the same or different—not what they are, just whether they’re the same.
If Truman measured the two photons individually, asking whether they’re horizontal or vertical, there are four possible outcomes. Both photons can be vertical (we write this as V1V2, where the first letter indicates the polarization of Photon 1 and the second that of Photon 2), both can be horizontal (H1H2), Photon 1 can be vertical and Photon 2 horizontal (V1H2), or Photon 1 can be horizontal and Photon 2 vertical (H1V2). These four outcomes will occur with different probabilities, depending on what the polarization of the original state was.
For teleportation, Truman doesn’t measure the individual polarizations, but instead asks whether they’re the same. This still gives four possible outcomes, two with the same polarization, and two with opposite polarizations. These “Bell states” are the allowed states for a pair of entangled photons, and when Truman makes his measurement, he’ll find Photons 1 and 2 in one of these four states:
These states are superpositions of the four possible outcomes from the independent measurements, just like Schrödinger’s famous cat is in a superposition of “alive” and “dead.”* Each of the polarizations is still indeterminate—if you go on to measure the individual polarization of Photon 1, you are equally likely to get horizontal or vertical. When you do measure Photon 1, you determine the state of Photon 2 to be either the same or opposite, depending on which of the four states you’re in.
“Wait a minute—why are there four outcomes? Shouldn’t there just be two? What’s with the pluses and minuses? Either they’re the same, or they’re not.”
“That’s true, but in quantum mechanics, there are two different states where they have the same polarization, State I and State II, and two where they have opposite polarizations, State III and State IV. That gives four states.”
“But what’s the difference between State I and State II?”
“They’re different states, in the same way that |V> + |H> and |V> – |H> are different states for a single photon.”
“Wait—they are?”
“Yes. You can see it by thinking of how they add together to give a single polarization at a different angle. You can imagine the |H> as being one step either left or right, and the |V> being one step either up or down. |V> + |H> is then one step up, and one to the right, while |V> – |H> is one step up, and one to the left.”
“So, |V> + |H> is 45º to the right of vertical, and |V> – |H> is 45º to the left of vertical?”
“Exactly. They both give a fifty-fifty chance of being measured as horizontal or vertical, but they’re different states. If you rotated your polarizer 45º clockwise, the |V> + |H> photons would all make it through, while the |V> – |H> photons would all be blocked.”
“So, State I is up and to the right, while State II is up and to the left?”
“Well, it’d be more complicated than that. There are two particles, so you’d need to do it in four dimensions, or something, but that’s the basic idea.”
“Okay, I suppose I’m convinced. Wait—you said the original two entangled photons need to have opposite polarizations. Shouldn’t they be in State III or IV, then?”
“You’re absolutely right. In the usual teleportation procedure, Photons 2 and 3 need to be in State IV. I didn’t mention that earlier, because I thought it would complicate things needlessly. Well spotted.”
“I’m a very clever dog. You can’t get anything past me.”
When Truman makes his measurement asking whether Photons 1 and 2 have the same polarization, Photons 1 and 2 are projected into one of these four states. At that instant, the entanglement between Photons 2 and 3 means that RD’s Photon 3 is put into a definite polarization state that depends on which state Truman measured. There are four possible results for the polarization of RD’s Photon 3, whose horizontal and vertical components are related to the horizontal and vertical components of Truman’s original Photon 1.
Each result is a simple rotation of the original polarization state—the arrows point in a different direction, but still involve a steps in one direction (up, down, left, or right), and b steps in another. Given the outcome of Truman’s measurement, RD knows how to recover the original state of Truman’s photon, even though he doesn’t know what that state was.
All Truman has to do, then, is phone RD and tell him the result of the measurement. At that point, RD knows exactly what he needs to do to get Photon 3 into the right state.
The state of RD’s Photon 3 after “teleportation,” for each of the four possible outcomes of Truman’s entangling measurement. Each state is a simple rotation of the initial polarization of Photon 1 (dotted arrow).
Based on the result of Truman’s measurement, RD can rotate the polarization of Photon 3, and know that he’s got exactly the state that Truman started with.
This scheme transfers the polarization state of Photon 1 to Photon 3, transforming it into a perfect copy of the initial state of Photon 1. In the process, though, the entangling measurement made on Photons 1 and 2 has changed the state of Photon 1 so that it is no longer in the same state as when it started—it’s in an indeterminate entangled state with Photon 2. It’s impossible for both dogs to end up with exactly the same state, satisfying the no-cloning theorem.
We also see that teleportation is not instantaneous. The polarization of Photon 3 is instantaneously determined when Truman makes the measurement on Photons 1 and 2, but there’s one more step, because Photon 3 is not instantaneously put into the correct state. Instead, it goes into one of four possible states, depending on the outcome of Truman’s measurement. The teleportation is not complete until RD makes the final rotation of Photon 3. RD can’t do that until he receives the message containing the outcome of the measurement, and that message has to travel from one dog to the other at a speed less than or equal to the speed of light.
TELEPORTING ACROSS THE DANUBE: EXPERIMENTAL DEMONSTRATION
The idea of teleportation was first proposed in 1993, and it was demonstrated in 1997 by a group in Innsbruck headed by Anton Zeilinger.* They produced their entangled photons by sending a photon from an ultraviolet laser into a special crystal that produces two infrared photons, each having half the energy of the original photon. They sent the laser through the crystal twice, to produce a total of four photons. One pair was used as the entangled pair needed for teleportation (Photons 2 and 3), while one of the other two was sent through a polarizer to provide the state to be teleported (Photon 1). The fourth photon was used as a trigger to let the experimenters know when to collect data.
Photons 1 and 2 were brought together on a beam splitter in a way that performed the entangling measurement. They could only detect one of the four Bell states, but when they did, they knew that Photon 3 was projected into a particular polarization. When they detected Photons 1 and 2 in State IV (25% of the time), they sent a signal to their analyzer to measure the polarization of Photon 3. Because they set the polarization of Photon 1 themselves, they were able to repeat the experiment many times, and confirm that Photon 3 was polarized at exactly the angle predicted by the teleportation protocol.
The initial demonstration used only one of the four possible Bell states in the measurement step, for reasons of experimental convenience, and teleported the polarization state all of half a meter. Subsequent experiments have expanded the measurements to include all four outcomes and extended the distance considerably. In 2004 the Zeilinger group teleported photons from one side of the Danube River* to the other (a distance of about 600 meters) over an optical fiber, showing that teleportation is practical over longer distances.*
Schematic of the Zeilinger group teleportation experiment. An ultraviolet laser passes through a downconversion crystal, where it produces two infrared photons (Photons 2 and 3), which serve as the entangled pair for teleportation. The ultraviolet laser then hits a mirror, and passes through the crystal again, producing another pair (Photons 1 and 4), one of which serves as the photon to be teleported, while the other is a trigger to let the experimenters know that all four photons have been produced. Photons 1 and 2 are brought together for an entangling measurement, and when they are found in the appropriate Bell state, the polarization of Photon 3 is measured to confirm the “teleportation.”
“Okay, but what’s the point?”
“What do you mean?”
“Well, who cares if you can teleport photon states?”
“Photons aren’t the only things whose states can be teleported. The maths is exactly the same for any two-state system, so you can use the same scheme to teleport the state of a single electron spin, for example, or transfer a particular superposition of two energy levels from one atom to another.”
“Yes, but if you can exchange the entangled atoms or electrons, why don’t you just send them, instead of teleporting them?”
“Atomic states and electron spins are sort of fragile, and it’s hard to send them long distances without the state getting messed up. What you can do is to take an atom, say, and entangle it with one photon from an entangled pair, and use the other photon to teleport the state of the first atom onto another atom in a distant place.”
“Okay, that’s a little better, but it’s still just one atom.”
“It doesn’t have to be. In 2006, a group at the Niels Bohr Institute in Copenhagen used teleportation to transfer a collective state from one group of atoms to another. There were about a trillion atoms in each of the two groups, which is still pretty small compared to dogs and people, but it shows that you can apply the technique to a larger system.”
“That still sounds pretty useless, but I suppose it’s getting better.”
“Thank you. You’re very kind.”
WHAT IS IT ALL FOR? APPLICATIONS OF TELEPORTATION
The quantum teleportation protocol lets us use entanglement to faithfully move a particular quantum state from one location to another, without physically moving the initial object. It can be used to reproduce photon states at distant locations, or to transfer a superposition state from one atom or group of atoms to another. Of course, it’s still a long way from the science fiction ideal.
As with the classical fax machine, the only thing transmitted is information. Quantum teleportation allows us to transfer a particular state or superposition of states from one place to another, in the same way that the fax machine allows us to send a facsimile of what’s printed on a paper document over telephone lines. If the state being “teleported” is the state of an atom, however, there have to be appropriate atoms waiting at the other end of the teleportation scheme, in the same way that the receiving fax machine needs to be loaded with paper and ink.
If the goal is to transfer an object from one place to another, though, it’s not obvious that you need quantum teleportation. Quantum teleportation moves a particular state from one place to another, but if you’re sending an inanimate object like a dog treat from one place to another, you may not need to preserve the exact state. As long as you have the right molecules in the right places relative to one another, it doesn’t make much difference to the taste or texture of the treat if the atoms in the facsimile treat are not in precisely the same states as the original. All you really need is a fax machine that works at the molecular level, and there’s nothing inherently quantum about that.
So why should we care about quantum teleportation? Quantum teleportation may not be needed to move inanimate objects, but it may be crucial for moving conscious entities. Some scientists believe that consciousness is essentially a quantum phenomenon—Roger Penrose, for example, promotes this idea in The Emperor’s New Mind. If they’re right, we would need a quantum teleporter, not just a fax machine, to move people or dogs, in order to properly reproduce their brain state. Quantum teleportation may be the key to ensuring that when Scotty beams you up to the Enterprise, you arrive thinking the same thoughts as when you left.
We’re not even close to teleporting people, though, so the current interest in quantum teleportation involves much smaller objects. Quantum teleportation is useful and important for situations where state information is the critical item that needs to be moved from one place to another. The primary application for this sort of thing today is in quantum computing.
A quantum computer, like the classical computers we use today, is essentially a large collection of objects that can take on two states, called “0” and “1.”* You can string these “bits” together to represent numbers. For example, the number “229” would be represented by eight bits in the pattern “11100101.”
In a quantum computer, however, the “qubits”† can be found not just in the “0” and “1” states, but in superpositions of “0” and “1” at the same time. They can also be in entangled states, with the state of one qubit depending on the state of another qubit in a different location. These extra elements let a quantum computer solve certain kinds of problems much faster than any classical computer—factoring large numbers, for example. The modern cryptography schemes used to encode messages—whether they’re government secrets or credit card transactions on the Internet—rely on factoring being a slow process. A working quantum computer might be able to crack these codes quickly, leading to intense interest in quantum computing from governments and banks.‡
The precise quantum state of an individual qubit is critical to the functioning of a quantum computer, and it’s here that quantum teleportation may find useful applications. A calculation involving a large number of qubits may require the entanglement of two qubits that are separated by a significant distance in the computer. Teleportation might be useful as a way of doing the necessary operations.
Further down the road, if we want to connect together two or more quantum computers in different locations, to make what Jeff Kimble of Caltech calls the “Quantum Internet,” schemes based on entanglement and teleportation may be essential. This would allow still greater improvements in computing, in the same way that the classical Internet does for everyday computers.*
Whatever its eventual applications, quantum teleportation is a fascinating topic. It shows us that the nonlocal effects of quantum entanglement and the “spooky action at a distance” explored in the EPR paper can be put to use, moving information around in a way that can’t be done by more traditional means. It may not help dogs to catch squirrels (not yet, anyway), but it’s another source of insight regarding the deep and bizarre quantum nature of the universe.
“I don’t know. I still think it’s rubbish.”
“Why’s that?”
“Well, I mean, if you call something ‘teleportation,’ I expect it to be good for more than just moving state information.”
“That is sort of unfortunate, I agree. I’m not the one who made up the name, though.”
“So, that’s it for entanglement, then? Just Aspect experiments and teleportation?”
“No, not at all. There are lots of things you can use quantum entanglement for. It’s the key to quantum computing, as I said, and you can use it for ‘dense coding,’ sending two bits of information for every one bit transmitted.”
“That’s still just moving information around.”
“There’s also quantum cryptography, where you use entanglement to transmit a string of random numbers from one person to another, numbers that they can then use to encode messages in a completely secure way. There’s no possibility of anyone eavesdropping on their messages, because the eavesdropping would change the particle states, and mess up the code in a way that can be detected.”
“Still just information.”
“Well, okay, but there are people who think that the proper way to think about quantum physics is in terms of information. In some sense, the whole science of physics is really all about information.”
“Really? Well, I’m a dog, and I’m all about getting squirrels.”
“Okay, but that’s really about information, too.”
“How so?”
“Well, for your information, there’s a big fat squirrel sitting right in the middle of the lawn.”
“Brilliant! Fat, squeaky squirrels!”
* We’ll talk about why he might want to do such an odd thing at the end of the chapter.
† Strictly speaking, a2 is the probability of finding vertical polarization, and b2 the probability of horizontal polarization and a2 + b2 = 1. So for a photon at 30° from the vertical, with a 75% chance of passing a vertical polarizer, a = 
and b = ½.
* Strictly speaking, then, before its state is measured, Schrödinger’s cat can be in one of two states: “alive plus dead,” or “alive minus dead.”
* The same Anton Zeilinger was seen in chapter 1 heading the group that demonstrated diffraction of molecules, and chapter 5 doing quantum interrogation. He has made a long and distinguished career doing experiments to demonstrate the weird and wonderful features of quantum mechanics.
* In the seven years between the two experiments, Professor Zeilinger moved from Innsbruck to Vienna.
* There’s no inherent problem with sending photons over very long distances—light manages to reach us from distant galaxies, after all—but interactions with the environment can destroy entangled states through the process of decoherence discussed in chapter 4. The Vienna experiment shows that decoherence can be avoided long enough to send entangled photons over useful distances.
* A classical computer uses millions of tiny transistors on silicon chips; quantum computers could use anything with at least two states—atoms, molecules, electrons.
† The “qu” is for “quantum.” Physicists are not widely admired for their ability to think up clever names.
‡ In fact, the National Security Agency is one of the largest funders of quantum computing research in the United States.
* Of course, it may also lead to quantum e-mail from dogs in Nigeria offering nine billion kilos of kibble if we’ll just provide the bank account information to help with a simple transaction …
