WHAT does a financial index have in common with Shakespeare's Richard III, a drawing of a cat and this sentence? Easy. No matter how important any one of them may be to you, they can all be reduced to the ubiquitous digital bits of the information age. And, as such, they can pass from a mind to a machine, flow down telephone lines and spill out unchanged onto a page halfway across the world. Information is nothing but patterns of 0s and 1s.

Or so everyone has believed. But now a growing band of physicists is putting forth a more alarming notion. They believe that information is a superweird new substance, more ethereal than matter or energy, but every bit as real and perhaps even more fundamental. For them, information is a kind of subtle substance that lies behind and beneath physical stuff. "Information is deeper than reality," says Anton Zeilinger, a physicist at the University of Innsbruck.

Zeilinger's shattering insight comes after years of studying information in the quantum world—one of the great challenges for frontier physicists. In the everyday world, information stays the same no matter how you choose to convey it. When driven into quantum terrain, however, it behaves oddly. Attach it to a quantum particle and suddenly it's everywhere and nowhere, on the edge of collapse and tricky beyond belief. In the past few years, this freakish behaviour has conjured up all sorts of exotic possibilities from Star Trek-style teleportation to quantum computing.

It may seem, then, as if information takes its quantum colours from the inhabitants of the quantum world on which it resides. But Zeilinger and others aren't so sure. Could it be the other way round? Quantum particles might be catching their behaviour from the information they contain. "By thinking this way," says Zeilinger, "we get a deeper grasp of quantum physics. And we begin to see that quantum theory is more than a theory of physics—it's a theory of information."

This new view of information was not born of any profound theoretical breakthrough, but has emerged from the minutiae of playing games with single particles. Take the act of tying information to an electron. An electron in a magnetic field has only two choices—it can spin clockwise or anti-clockwise about the direction of the field. Physicists call these states "up" or "down" because the electron's spin makes it act like a tiny upward or downward pointing magnet. Call one of these states "0" and the other "1", and an electron's spin naturally stores one bit.

A two-state quantum system like this is called a "qubit," and doesn't seem so different from an ordinary bit. Yet as the building blocks of information in the quantum world, qubits are very far from ordinary. While the spin of an electron is always up or down when you measure it, it does more adventurous things when you don't. A quantum particle can split its existence and enter into a "superposition" of states where it simultaneously has one existence with spin up and another with spin down (see Diagram). So a qubit can store a 0 or 1, but can also mingle these two in varying proportions to produce any of an infinite number of more bizarre quantum states.

Qubits demolish another expectation: two electrons, you might think, make two qubits. But no. Instead, those electrons can enter into an "entangled state", a kind of union in which neither has a separate existence. If two electrons have entangled spins, then if one is up, the other is always down(see Diagram). "In an entangled state," says Charles Bennett of the IBM Research Division in Yorktown Heights, New York, "distant particles are linked in a way that they classically couldn't be unless they were in the same place." Entangled electrons are no longer independent, and so cannot store two qubits.

Superposition and entanglement affect anything that ventures into the quantum world. Over the past few years, Bennett has led physicists' attempts to understand the subtle behaviour of information when it lives under such weird conditions. If you try to handle information the way you would normally, the quantum world brings nothing but trouble. Suppose you want to read some information and move it from one place to another—a trivial task in the classical world. Ten electrons can store 10 qubits of quantum information. To read it out and move it over to another identical set of electrons, you would first measure the exact quantum state of every electron, and then set the receiving electrons into the same states.

Trouble is, quantum theory prohibits even the first part of the act—measuring the exact state of a quantum system. "You can't make copies of quantum information," says Bennett. Why? Because if you measure an electron's spin, it always comes out up or down even if the electron was in a superposition of the two. Superpositions collapse irreversibly upon measurement, so you can't know what the electron's state was just before you looked at it.

And yet, these restrictions are also tools which can be used to spectacular effect. Suppose that you wanted to fax something from, say, London to New York. With conventional information, a page of text is no trouble. But what if you wanted to fax a cup of coffee? Impossible? Not if you use quantum information.

To recreate your cup of coffee you need to transmit the exact quantum state of every particle in it. So what you need is a teleportation machine—a super souped-up fax that can read and send quantum information. All it would have to do is find out the states of the particles in London. After transferring that information across the ocean, it would inject it into another set of particles. Out would pop a replica cup of coffee in New York.

In 1993, Bennett used the equations of quantum theory to show that entanglement, in principle, provides a way to make such a teleportation device. Even though quantum information cannot be copied or read, there is still a way to send it from one place to another—you just can't know what it is you're sending. Zeilinger and his colleagues at Innsbruck have now put Bennett's ideas into practice, and are routinely teleporting single photons around their lab.

Weird link

In Bennett's scheme, the working channel for teleporting a photon is an entangled pair of subsidiary photons: A at the sending station and B at the receiving station. The "message" photon to be teleported, C, is also located at the sending station (see Diagram). The goal is to copy the quantum state of photon C into that of photon B, effectively moving photon C across the gap and into B's spot, even though C never really moves physically.

You can't just measure the state of C and send that information across. For as soon as you measure a quantum state, any superposition collapses. The information locked in a quantum state is unwieldy, and in trying to measure it, you cannot help losing a portion and ending up with only a fragment of that needed to describe the original state of the particle.

Bennett's idea is to use entanglement to recapture the disappearing portion of the quantum information. "It is resource for communication," he says. For the entangled pair A and B can be used as a tool to move C's information across to B.

In their experiment, Zeilinger and his colleagues first measure a combined property of photons A and C. This yields a piece of information about C, with some information about A mixed in. However, the quantum information about C does not vanish when the measurement causes the superposition to collapse. Remember that A and B are entangled, so measuring A affects the state of B. The result, and this is the clever part, is that measuring A and C together directs the missing quantum information about C to slip down the entanglement line to B.

The punchline? Transport the piece of incomplete information that you hold about C down to where B is, and you can construct a particle that's identical to the original C. This is the trick that Zeilinger's team pulled off late last year and reported in Nature (vol 390, p 575).

If it were possible to realise the same stunt with bigger things—by teleporting all of their particles—then one day you might be able to teleport money, cups of coffee or even yourself from one city to another. The practical barriers to doing it, however, are formidable. The weird quantum link between entangled particles is extraordinarily tenuous, and breaks—in a process known as "decoherence"—if even so much as a single wayward atom disturbs one of the particles. To maintain the entanglement, the particles need to be isolated from the rest of the world— a nearly impossible challenge for any lab. Still, Zeilinger believes that atoms, molecules and even small viruses may be teleported within a decade or so.

The other great hope for quantum information is in computing. When an ordinary computer runs through a computation, its bits flip through a series of patterns of 0s and 1s in the process of transmitting information. But imagine replacing every bit in an ordinary computer with a single electron, and storing information in its spin. Each qubit could be either 0 or 1 or a superposition of the two. Putting qubits together makes their superpositions multiply. A trio of bits, each in the in between state, would lend part of its existence to the 000 state, another to the 111 state, and share out other slivers to the other combinations—001, 010, 011, 100, 101 and 110.

As the number of bits increases, the number of existences grows exponentially. With 16 bits, there are 65 536. And with 32 bits, over 4 billion. So through quantum parallelism, a computer with 32 bits could split into more than a billion computers working side by side, each following a different computational trajectory.

Living with noise

Some of Bennett's colleagues at IBM have worked out just how powerful quantum computers could be. Four years ago, Peter Shor proved that a quantum computer could in seconds factor numbers so large that ordinary computers would labour for months in the effort. And last year, Lou Grover, also of IBM, showed that a quantum machine could sort through lists—such as telephone directories or huge databases—far more effectively than classical computers.

Like teleportation, quantum computing has only been done so far with two qubits (see "Wake up to quantum coffee", New Scientist, 15 March 1997, p 28). Obviously, preventing decoherence is the main obstacle to scaling the process up, and making these flights of the imagination practicable. There is some doubt that it will ever be done. "I'm most sceptical of computing," says Rolf Landauer, another IBM researcher, "because quantum parallelism is the most demanding of these things."

Almost any disturbance, no matter how weak, will ruin a quantum superposition and spoil the parallelism it permits. And since noise and imperfection are ever-present in the real world, decoherence would seem almost unavoidable. Zeilinger, however, remains optimistic. "I'm convinced that we will have a new information technology in the future, and that it will use quantum technology," he says.

Fuelling his confidence are a host of new mathematical tricks that physicists are devising to preserve quantum coherence even in hostile surroundings. They are not struggling after the hopeless goal of perfect isolation from the environment. A computer will inevitably receive some unexpected shocks from the outside world. And they will cause errors. The point is to learn how to correct them.

In 1995, Shor and physicist Andrew Steane of Oxford University independently showed that a quantum computer could be designed so that disturbances from the outside world wouldn't be fatal. By encoding the information in "error-correcting codes", additional operations in the computer can be made to counter any mistakes, and repair their damage. "Error correction achieves the apparently impossible," says Steane, "since a computation can preserve quantum coherence even though during its course every qubit in the computer will have relaxed many times."

Of course, it is not only shocks from the outside that can cause problems. Even if perfectly isolated, the working parts of any computer will sometimes fail. What if an error occurs on the inside, during some of the crucial error-correcting steps themselves? Physicists Emanuel Knill, Raymond Laflamme and Wojciech Zurek from the Los Alamos National Laboratory in New Mexico have now shown that this isn't necessarily a problem either. In a paper published last month in Science (vol 279, p 342) they showed how a quantum computer could be designed to be "fault tolerant", so that as long as the noise level in the computer was kept below some reasonable level, effective error correction would be possible in real devices.

Quantum landscape

But practical uses may not be the most remarkable or lasting consequences of the quantum view on information. Why is the quantum world as weird as it is? This may seem like an unanswerable question. Or, perhaps the quantum landscape is the way it is because it must conform to the laws of some deeper level where information is supreme. If so, information would truly be the most fundamental level of reality.

This possibility becomes quite plausible when you start to think about the smallest possible pieces of quantum information, one of which is the qubit. Does entanglement also have a smallest unit? Bennett thinks so. In 1996, he and other researchers introduced the idea of "the amount of entanglement in a maximally entangled pair". They called it an ebit—a single "particle" of entanglement. Thinking of qubits and ebits as "particles" of information shows just how much quantum information is beginning to look like real matter. And the analogy can be pushed quite far.

Ordinarily, we think of space as being empty. And yet according to quantum theory, it is in fact filled with "virtual" pairs of electrons, positrons and other quantum particles which flit constantly in and out of existence. A virtual particle is not real, because it must borrow its energy from the vacuum. By Heisenberg's uncertainty principle, it can do this for a short time only, and must then give its energy back and vanish. As a result, these particles only exist briefly, and only make their presence known if they interact with a real particle before vanishing.

At the California Institute of Technology, Nicolas Cerf and Chris Ademi picture an ebit as representing a kind of "virtual" information. In traditional information theory, information is always real—just as energy is in classical physics. In quantum theory, however, information can become virtual. The act of entangling a pair of particles corresponds to creating a virtual pair of information particles—a qubit and an anti-qubit—out of the information vacuum.

And just as virtual particles are revealed through their interactions with real particles, so with virtual information. It only has consequences when one member of the entangled pair interacts with real information. Particle physicists like to use Feynman diagrams to chart the flow of particles through space, and the same can be done with quantum information. Teleportation, Cerf and Ademi find, is closely analogous to the process whereby a real electron scatters off a virtual electron-positron pair (see Diagram).

One way such an interaction can occur is by the electron first colliding with and annihilating the positron. This makes a photon which combines with the other virtual electron to make a real electron—the outgoing particle. Similarly, in teleportation, a qubit can interact with one ebit of an entangled pair, creating real information. This then travels onwards to interact with the anti-ebit at the receiving point, remaking the original qubit.

So in the context of quantum theory, information and physical stuff are beginning to blur into a kind of supersubstance that goes beyond the properties of either. "Information is such a fundamental thing," says Steane. "The ambitious goal is to discover its basic properties, and then from that deduce quantum theory."

There's no telling where this kind of thinking will lead.

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