How to Teach Physics to Your Dog (24 page)

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.

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.

Schematic of the Zeilinger group teleportation experiment. An ultra-violet 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.”

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.
^†

“Yeah, 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 tele-ported. The math 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.”

“Yeah, 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 kind 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 guess it’s getting better.”

“Thank you. You’re very kind.”

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, dude. I still think it’s lame.”

“How’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 kind 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, sure, 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.”

“Yeah? 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.”

“Ooooh! Fat, squeaky squirrels!”

*
We’ll talk about why he might want to do such an odd thing at the end of the chapter.

†
Of course, it may also lead to quantum e-mail from dogs in Nigeria offering nine billion pounds of kibble if we’ll just provide the bank account information to help with a simple transaction . . .

†
Strictly speaking,
a
²
is the probability of finding vertical polarization, and
b
²
the probability of horizontal polarization and
a
²
+
b
²
= 1. So for a photon at 30° from the vertical, with a 75% chance of passing a vertical polarizer,
, and b = 1/2.