**THE FABRIC of the COSMOS,****Brian Greene,**2004

```(annotated and with added

**bold highlights by Epsilon=One**)

**Chapter 15 - Teleporters and Time Machines**

Quantum Entanglement and Quantum Teleportation

In 1997, a group of physicists led by Anton Zeilinger, then at the University of Innsbruck, and another group led by A. Francesco De Martini at the University of Rome,

Remember, two entangled particles, say two photons, have a strange and intimate relationship. While each has only a certain probability of spinning one way or another, and while each, when measured, seems to "choose" randomly between the various possibilities,

Nevertheless, even though

The reasoning behind this conclusion, while mathematically straightforward is cunning and ingenious. Here's the flavor of how it goes.

Imagine I want to teleport a particular photon, one I'll call Photon A, from my home in New York to my friend Nicholas in London. For simplicity let's see how I'd teleport the exact quantum state of the photon's spin — that is; how I'd ensure that Nicholas would acquire a photon whose probabilities of spinning one way or another were identical to Photon A's.

I can't just measure the spin of Photon A, call Nicholas, and have him manipulate a photon on his end so its spin matches my observation; the result I find would be affected by the observation I make, and so would not reflect the true state of Photon A before I looked. So what can I do? Well, according to Bennett and colleagues, the first step is to ensure that Nicholas and I each have one of two additional photons, let's call them Photons B and C, which are entangled. How we get these photons is not particularly important. Let's just assume that Nicholas and I are certain that even though we are on opposite sides of the Atlantic, if I were to measure Photon B's spin about any given axis, and he were to do the same for Photon C, we would find exactly the same result.

The next step, according to Bennett and coworkers, is

The distant Photon C is entangled with Photon B, so if I know how Photon A is related to Photon B, I can deduce how Photon A is related to Photon C. If I now phone this information to Nicholas, communicating how Photon A is spinning relative to his Photon C, he can determine how Photon C must be manipulated so that its quantum state will match Photon A's. Once he carries out the necessary manipulation, the quantum state of the photon in his possession will be identical to that of Photon A, and that's all we need to declare that Photon A has been successfully teleported. In the simplest case, for example, should my measurement reveal that Photon B's spin is identical to Photon A's, we would conclude that Photon C's spin is also identical to Photon A's, and without further ado, the teleportation would be complete. Photon C would be in the same quantum state as Photon A, as desired.

Well, almost. That's the rough idea, but to explain quantum teleportation in manageable steps, I've so far left out an absolutely crucial element of the story, one I'll now fill in. When I carry out the joint measurement on Photons A and B, I do indeed learn how the spin of Photon A is related to that of Photon B. But, as with all observations, the measurement itself affects the photons. Therefore, I do not learn how Photon A's spin was related to Photon B's before the measurement. Instead, I learn how they are related after they've both been disrupted by the act of measurement. So, at first sight, we seem to face the same quantum obstacle to replicating Photon A that I described at the outset: the unavoidable disruption caused by the measurement process. That's where Photon C comes to the rescue. Because Photons B and C are entangled, the disruption I cause to Photon B in New York

And that's fantastically interesting. Through my measurement, we are able to learn how Photon A's spin is related to Photon B's, but with the prickly problem that both photons were disrupted by my meddling. Through entanglement, however, Photon C is tied in to my measurement — even though it's thousands of miles away — and this allows us to isolate the effect of the disruption and thereby have access to information ordinarily lost in the measurement process. If I now call Nicholas with the result of my measurement, he will learn how the spins of Photons A and B are related after the disruption, and, via Photon C, he will

As you can see, quantum teleportation involves two stages, each of which conveys critical and complementary information. First, we undertake a joint measurement on the photon we want to teleport with one member of an entangled pair of photons. The disruption associated with the measurement is imprinted on the distant partner of the entangled pair through the

Notice, as well, a couple of key features of quantum teleportation. Since Photon A's original quantum state was disrupted by my measurement,

Implementing this strategy for quantum teleportation was no small feat. By the early 1990s, creating an entangled pair of photons was a standard procedure, but carrying out a joint measurement of two photons (the joint measurement on Photons A and B described above, technically called a

**each carried out the first successful teleportation of a single photon. In both experiments, an initial photon in a particular quantum state was teleported a short distance across a laboratory, but***2***there is every reason to expect that the procedures would have worked equally well over any distance.**Each group used a technique based on theoretical insights reported in 1993 by a team of physicists — Charles Bennett of IBM's Watson Research Center; Gilles Brassard, Claude Crepeau, and Richard Josza of the University of Montreal; the Israeli physicist Asher Peres; and William Wootters of Williams College — that rely on quantum entanglement (Chapter 4).Remember, two entangled particles, say two photons, have a strange and intimate relationship. While each has only a certain probability of spinning one way or another, and while each, when measured, seems to "choose" randomly between the various possibilities,

**whatever "choice" one makes the other immediately makes too, regardless of their spatial separation.**In Chapter 4, we explained that there is no way to use entangled particles to send a message from one location to another faster than the speed of light. If a succession of entangled photons were each measured at widely separated locations, the data collected at either detector would be a random sequence of results (with the overall frequency of spinning one way or another being consistent with the particles' probability waves). The entanglement would become evident only on comparing the two lists of results, and seeing, remarkably, that they were identical. But that comparison requires some kind of ordinary, slower-than-lightŽspeed communication. And since before the comparison no trace of the entanglement could be detected, no faster than light-speed signal could be sent.Nevertheless, even though

**entanglement can't be used for superluminal communication, one can't help feeling that long-distance correlations between particles are so bizarre that they've got to be useful for something extraordinary. In 1993, Bennett and his collaborators discovered one such possibility. They showed that quantum entanglement could be used for quantum teleportation. You might not be able to send a message at a speed greater than that of light, but if you'll settle for slowerŽthan-light teleportation of a particle from here to there, entanglement's the ticket.**The reasoning behind this conclusion, while mathematically straightforward is cunning and ingenious. Here's the flavor of how it goes.

Imagine I want to teleport a particular photon, one I'll call Photon A, from my home in New York to my friend Nicholas in London. For simplicity let's see how I'd teleport the exact quantum state of the photon's spin — that is; how I'd ensure that Nicholas would acquire a photon whose probabilities of spinning one way or another were identical to Photon A's.

I can't just measure the spin of Photon A, call Nicholas, and have him manipulate a photon on his end so its spin matches my observation; the result I find would be affected by the observation I make, and so would not reflect the true state of Photon A before I looked. So what can I do? Well, according to Bennett and colleagues, the first step is to ensure that Nicholas and I each have one of two additional photons, let's call them Photons B and C, which are entangled. How we get these photons is not particularly important. Let's just assume that Nicholas and I are certain that even though we are on opposite sides of the Atlantic, if I were to measure Photon B's spin about any given axis, and he were to do the same for Photon C, we would find exactly the same result.

The next step, according to Bennett and coworkers, is

*not*to directly measure Photon A — the photon I hope to teleport — since that turns out to be to drastic an intervention. Instead, I should measure a*joint*feature of Photon A and the entangled Photon B. For instance, quantum theory allows me to measure whether Photons A and B have the same spin about a vertical axis, without measuring their spins individually. Similarly, quantum theory allows me to measure whether Photons A and B have the same spin about a horizontal axis, without measuring their spins individually. With such a joint measurement, I do not learn Photon A's spin, but I do learn how Photon A's spin is related to Photon B's. And that's important information.The distant Photon C is entangled with Photon B, so if I know how Photon A is related to Photon B, I can deduce how Photon A is related to Photon C. If I now phone this information to Nicholas, communicating how Photon A is spinning relative to his Photon C, he can determine how Photon C must be manipulated so that its quantum state will match Photon A's. Once he carries out the necessary manipulation, the quantum state of the photon in his possession will be identical to that of Photon A, and that's all we need to declare that Photon A has been successfully teleported. In the simplest case, for example, should my measurement reveal that Photon B's spin is identical to Photon A's, we would conclude that Photon C's spin is also identical to Photon A's, and without further ado, the teleportation would be complete. Photon C would be in the same quantum state as Photon A, as desired.

Well, almost. That's the rough idea, but to explain quantum teleportation in manageable steps, I've so far left out an absolutely crucial element of the story, one I'll now fill in. When I carry out the joint measurement on Photons A and B, I do indeed learn how the spin of Photon A is related to that of Photon B. But, as with all observations, the measurement itself affects the photons. Therefore, I do not learn how Photon A's spin was related to Photon B's before the measurement. Instead, I learn how they are related after they've both been disrupted by the act of measurement. So, at first sight, we seem to face the same quantum obstacle to replicating Photon A that I described at the outset: the unavoidable disruption caused by the measurement process. That's where Photon C comes to the rescue. Because Photons B and C are entangled, the disruption I cause to Photon B in New York

*will also be reflected in the state of Photon C in London.*That is the wondrous nature of quantum entanglement, as elaborated in Chapter 4. In fact, Bennett and his collaborators showed mathematically that through its entanglement with Photon B, the disruption caused by my measurement*is imprinted on the distant Photon C.*And that's fantastically interesting. Through my measurement, we are able to learn how Photon A's spin is related to Photon B's, but with the prickly problem that both photons were disrupted by my meddling. Through entanglement, however, Photon C is tied in to my measurement — even though it's thousands of miles away — and this allows us to isolate the effect of the disruption and thereby have access to information ordinarily lost in the measurement process. If I now call Nicholas with the result of my measurement, he will learn how the spins of Photons A and B are related after the disruption, and, via Photon C, he will

*have access to the impact of the disruption itself.*This allows Nicholas to use Photon C to, roughly speaking, subtract out the disruption caused by my measurement and thus skirt the obstacle to duplicating Photon A. In fact, as Bennett and collaborators show in detail, by at most a simple manipulation of Photon C's spin (based on my phone call informing him how Photon A is spinning relative to Photon B) Nicholas will ensure that Photon C, as far a its spin goes, exactly replicates the quantum state of Photon A*prior to my measurement.*Moreover, although**spin is only one characteristic of a photon, other features of Photon A's quantum state (such as the probability that it has one energy or another) can be replicated similarly.**Thus, by using this procedure, we could teleport Photon A from New York to London.*3*As you can see, quantum teleportation involves two stages, each of which conveys critical and complementary information. First, we undertake a joint measurement on the photon we want to teleport with one member of an entangled pair of photons. The disruption associated with the measurement is imprinted on the distant partner of the entangled pair through the

**weirdness of quantum nonlocality.**That's Stage 1, the distinctly quantum part of the teleportation process. In Stage 2, the result of the measurement itself is communicated to the distant reception location by more standard means (telephone, fax, e-mail . . .) in what might be called the classical part of the teleportation process. In combination, Stage 1 and Stage 2 allow the exact quantum state of the photon we want to teleport to be reproduced by a straightforward operation (such as a rotation by a certain amount about particular axes) on the distant member of the entangled pair.Notice, as well, a couple of key features of quantum teleportation. Since Photon A's original quantum state was disrupted by my measurement,

*Photon C in London is now the only one in that original state.*There aren't two copies of the original Photon A and so, rather than calling this quantum faxing, it is indeed more accurate to call this quantum teleportation.**Furthermore, even though we teleported Photon A from New York to London — even though the photon in London becomes indistinguishable from the original photon we had in New York — we do not learn Photon A's quantum state. The photon in London has exactly the same probability of spinning in one direction or another as Photon A did before my meddling, but we do not know what that probability is. In fact, that's the trick underlying quantum teleportation. The disruption caused by measurement prevents us from determining Photon A's quantum state, but in the approach described,***4**we don't need to know the photon's quantum state in order to teleport it.*We need to know only an aspect of its quantum state — what we learn from the joint measurement with Photon B. Quantum entanglement with distant Photon C fills in the rest.Implementing this strategy for quantum teleportation was no small feat. By the early 1990s, creating an entangled pair of photons was a standard procedure, but carrying out a joint measurement of two photons (the joint measurement on Photons A and B described above, technically called a

*Bell-state measurement*) had never been attained. The achievement of both Zeilinger's and De Martini's groups was to invent ingenious experimental techniques for the joint measurement and to realize them in the laboratory.**By 1997 they had achieved this goal, becoming the first groups to achieve the teleportation of a single particle.***5*