By Tom Siegfried
Science Editor of The Dallas Morning News
Like the fog on little cat feet, a new field of scientific research has crept into existence in the 1990s, almost unnoticed outside a small group of specialists who apply quantum physics to the study of information.
The new field, quantum information theory, addresses deep questions about information processing and the laws of nature. Surprising new findings have shown how such research could someday have important practical uses, such as in cracking secret codes or designing super-powerful computers.
If such "quantum" computers can actually be built, quantum information theory will be essential to understanding their capabilities. The impact of such devices may be far in the future but would be widespread, affecting the worlds of communication, finance and the military as well as the computer industry.
"Quantum information theory's a pretty new game," said Benjamin Schumacher, a physicist at Kenyon College in Gambier, Ohio. "Five years ago there wasn't such a thing. Now there is, sort of."
At a meeting in Santa Fe last month, experts from around the world discussed the latest findings in the field and its possible implications, both for real-life problems and for understanding nature more deeply.
"There now seems to be a critical mass of scientists working on this, and lots of interesting results are coming out of it," says Seth Lloyd, a physicist at the Santa Fe Institute, an interdisciplinary research organization.
A centerpiece of the new science is Dr. Schumacher's invention of a unit of quantum information called the qubit, introduced into physics lingo in 1992 at a meeting in Dallas, Qubits (pronounced CUE-bits) are the quantum cousins of bits, the units of information processed by ordinary computers.
In a theorem soon to be published in the journal Physical Review A, Dr. Schumacher has shown how measuring qubits provides a way to compute the least amount of resources needed to transmit a given quantum message. A quantum message is typically carried by particles of light prepared under special conditions.
"What the theorem tells you is how good you could do in quantum data compression," Dr. Schumacher said in an interview.
The need for a special unit of quantum information reflects the profound differences between quantum physics and traditional or "classical" physics. Quantum laws, as codified in the mathematical framework known as quantum mechanics, describe a ghostlike world of many possible realities. In the quantum realm, particles behave like waves, smeared out over space instead of occupying a definite location.
This quantum nature of matter and energy has been known and studied for most of the 20th century. But the role of quantum physics in information theory has attracted substantial scientific interest only in the 1990s.
"Nobody was working on this a few years ago," said Charles Bennett of IBM'S Watson Research Center in Yorktown Heights, NY. "Now we're really able to make progress in understanding...all the different ways in which classical and quantum information can interact, in what cases one can be substituted for another, and how many bits or qubits you need to transmit certain kinds of messages."
Ordinary information comes in many forms - such as pictures, words on paper, or Morse code. Whatever the form, such information can always be translated into a sequence of 0s or 1s. Each such digit is a bit. In general terms, a bit is simply a choice of one of two possibilities, like 0 or 1, heads or tails. Analyzing the properties of information in terms of bits is at the heart of classical information theory, invented in the 1940s by Claude Shannon of Bell Labs.
Qubits turn out to be quite a bit more complicated than ordinary bits. A qubit can be 0, 1, or a fuzzy combination of both 0 and 1, like a spinning coin that has not yet landed.
"Quantum information," says physicist Richard Jozsa, "is a rather curious thing."
The curious features of quantum information have begun to attract the attention of scientists whose jobs involve information processing and communication, said Carlton Caves, a physicist at the University of New Mexico in Albuquerque.
"The excitement is that the whole nature of information in quantum mechanics appears to be different than it is in classical physics," he said.
For example, classical information, like ink on paper or magnetic patterns on floppy disks, can be easily copied, leaving the original unperturbed. And it can be duplicated over and over again, at least until the copying machine breaks down. But information in the form of a quantum particle cannot be copied even once. Simply looking at quantum information destroys or disrupts it.
"Quantum information is fragile. It cannot be duplicated without distortion," says Asher Peres, a quantum physicist at the Israel Institute of Technology in Haifa.
"Yet despite that, it's terribly useful," insists Dr. Jozsa, of the University of Plymouth in England.
At least it could be useful, someday. The weirdness of quantum information could, on the one hand permit quantum computers to crack today's toughest secret codes. On the other hand, it could enable quantum communicators to devise a foolproof secret message system.
Studying quantum information might also help physicists explain some of the deep mysteries of quantum physics and the nature of reality. Most of these achievements, however, would require a device that so far exists only in physicists' imaginations - a quantum computer.
In today's computers, the standard rules of classical information theory govern how information is stored, retrieved and processed. But for hypothetical quantum computers, the rules of information processing are vastly different.
Ordinary computers calculate one step at a time. Computing elements can be connected in parallel to carry out many, but still a limited number, of computations at once. In contrast a quantum computer could carry out an almost countless number of calculations concurrently. In the end, though, a quantum computer could deliver only one answer. That's because looking at quantum information disturbs it, and in the case of a quantum computer, only one result would survive in nonquantum form.
It's a little like a human brain simultaneously holding many fuzzy thoughts - perhaps contradictory possible actions - when ultimately only one of those thoughts can be translated into a definite act.
The multiple quantum computations take place in a mathematical twilight zone known as Hilbert space. That's the realm containing all the fuzzy possibilities of quantum mechanical math. A quantum computer could show that Hilbert space is somehow real, not a mere convenient mathematical fiction.
Until recently, it was unclear whether a quantum computer using those multiple possibilities could really solve a useful problem any faster than a conventional computer could.
But last year Umesh Vazirani and Ethan Bernstein devised a mathematical problem that could be solved somewhat faster on a quantum computer. Daniel Simon at the University of Montreal then showed mathematically that a quantum computer could solve a problem very much more rapidly than an ordinary computer.
At last month's conference, sponsored by the Santa Fe Institute, the University of New Mexico and Los Alamos National Laboratory, several discussions focused on the potential use of quantum computers for cracking secret codes.
Many such codes, used for financial transactions or military secrets, make use of what is called a "public key," which provides the information needed to translate a message into coded form. Such a key requires the use of a very large number, more than 100 digits long. Anyone knowing that number can send a coded message.
To decipher the coded message, however, a spy would need a second key. That key requires knowledge of which prime numbers, multiplied together, produce the original long key number. Prime numbers, such as 37, 43 or 101, can be divided without remainder only by 1 and themselves.
Current codes are secure because breaking a huge number into its prime factors is extraordinarily difficulty. Teams of researchers working on 1,600 separate computers recently found the primes for a 129-digit code number. a task taking eight months.
But a longer number, say 2,000 digits, could not be cracked by any traditional method.
"It's not just a case that all the computers in the world today would be unable to factor that number," said Dr. Vazirani, of the University of California, Berkeley. "It's really much more dramatic...Even if you imagine that every particle in the known universe was a computer and was computing at full speed for the entire known life of the universe, that would be insufficient time to factor that number."
In mid-April, though, mathematician Peter Shor of AT&T Bell Labs began to circulate a stunning new analysis showing how such a huge number could be broken down into its factors quickly - using a quantum computer.
"Currently, nobody knows how to build a quantum computer," Dr. Shor noted in a paper that has been hopping around the country via a form of classical information transmission, e-mail. "It is hoped that this paper will stimulate research on whether it is feasible to actually construct one."
Specifically, Dr. Shor showed how the factoring problem could be formulated in a way similar to the problems described by Drs. Simon, Vazirani and Bernstein.
In essence, making use of the multiple quantum realities in Hilbert space would allow a quantum computer to perform an essential aspect of the factoring process in a tiny fraction of the time required by ordinary computers. The single result produced by the quantum computer would be precisely the number a mathematician would need to find the prime factors.
"This is the first really useful problem that has been shown to be solvable on a quantum computer," said Dr. Vazirani. "It's a truly dramatic result."
For banks and spy agencies that fear their codes will someday be worthless, the quantum information theorists have a ready answer - quantum cryptography.
Quantum factoring of large numbers poses a problem because those large numbers - used as keys for encoding messages - are distributed publicly. Using quantum cryptography, the encoding key could be transmitted secretly.
"If quantum factoring is successful, then you have a key distribution problem," said Artur Ekert of Oxford University in England. "That is exactly what quantum cryptography solves."
Quantum cryptography relies on the fact that looking at quantum information disrupts it. So a spy intercepting a quantum message would inevitably alter it in such a way that eavesdropping could always be detected.
Several physicists, among them Dr. Ekert, Dr. Bennett, Dr. Jozsa, Dr. Peres, and Gilles Brassard of the University of Montreal, have explored additional aspects of quantum cryptography. Such studies have outlined systems that would seem to permit coded communication immune to eavesdropping. Those systems would employ an elaborate process of sending quantum messages through one channel, such as optical fiber, and comparing notes sent over an ordinary channel, such as a telephone. In that way, two communicators could secretly exchange a string of bits that could then be used as the key for a secret code.
Already, working models of quantum cryptography systems have been built, and the ability to transmit quantum particles has been tested over distances of more than five miles, Dr. Bennett said.
An offshoot of quantum cryptography research is quantum teleportation - transmitting quantum information to a distant recipient. The name suggests that "teleporting" quantum information could be the forerunner of a science-fictionish transportation system a few hundred years from now. But more likely, and probably sooner, it could be used to transfer quantum information from one computer to another.
If a quantum computation is under way in one computer, teleportation could send the unfinished computation to another computer to finish the job, without losing any quantum information in the process, Dr. Jozsa pointed out.
Dr. Jozsa, Bennett and Peres were among six co-authors of a paper last year published in Physical Review Letters outlining the basics of a quantum teleportation system.
For now, the transporters of the Starship Enterprise will require special effects, and banks and spies do not yet need to trash their codes. Quantum computers are still dreams, and some experts find them dreams that are too good to come true. Even though it now appears that a quantum computer could solve practical problems, the practical problems of building a quantum computer might just be too difficult to overcome.
Rolf Landauer, an IBM computer physicist, warns that unless everything works perfectly, a quantum computer won't work at all. "And nature abhors perfection," he said at the Santa Fe conference.
For one thing, to perform many simultaneous computations, a quantum computer requires almost total isolation from the environment. Any observation or interaction with the outside world of the slightest kind would eradicate the multiple computations.
For another thing, Dr. Landauer points out in a paper to be published by the Proceedings of the Royal Society of London, manufacturing imperfections will cause a quantum computer to deviate from the precise processes envisioned by quantum mathematics. These defects will likely abort the computations before it is completed. Furthermore, the small errors that inevitably occur during the computational process cannot be corrected without loss of the multiple quantum computations, Dr. Landauer noted.
So on the one hand, a quantum computer must be designed so that its elements are very unlikely to interact with anything. Yet to compute, the elements must interact with each other. It would be difficult to build a device that accommodates both requirements.
"Full-blown quantum computation that will allow one to factor large numbers rapidly is probably far in the future in terms of real devices," said Dr. Lloyd of the Santa Fe Institute. "I would be surprised if I saw a quantum computer do this in our lifetime. But at least it doesn't seem impossible."
On the other hand, small-scale working-model quantum computers might be feasible within a few years, said Dr. Lloyd, who last year proposed a possible scheme for quantum computing, published in the journal Science.
Basically, his proposal involves shooting pulses of light into a crystal or other suitable material to manipulate the quantum information stored by particles within the material.
Whether such a device could operate very long before succumbing to imperfections isn't yet clear. However, quantum computers would be so powerful that if one could work for only a short time, it might still be useful.
"Even if you can build a small-size quantum computer that can last without errors for a few hundred thousand steps, that would be an enormous achievement," said Dr. Vazirani.
While the prospect of quantum computers that could solve real-world problems has suddenly made quantum information theory more relevant to everyday concerns, it has also spurred new interest in fundamental questions about the meaning of quantum physics.
In principle, quantum mechanics applies to the entire universe, but its weird fuzzy effects are generally noticeable only in the realm of atoms and molecules. In that world of the very small, though, there is no doubt about it - quantum mechanics' strange predictions always come true.
"Quantum mechanics is weird," said Dr. Lloyd. "That's an experimental fact. Everybody finds it weird...It involves features that are hard to understand."
Niels Bohr, the Danish physicist who pioneered the establishment of quantum physics during the early decades of the 20th century, once said that anyone studying quantum mechanics without becoming dizzy hasn't understood it. Quantum information theory, Dr. Lloyd said, is helping scientists to "explore the strange aspects of quantum mechanics without becoming dizzy.
"These different ideas about...how information can be processed and used in a purely quantum mechanical fashion are good ways of figuring out just where the weirdness in quantum mechanics lies," he said.
Dr. Schumacher sees profound insights emerging from quantum information theory. In particular, he suggests, the impossibility of copying quantum information may be at the root of many quantum mysteries.
The no-copy feature of quantum information was discovered more than a decade ago by Wojciech Zurek, now of the Los Alamos National Laboratory, and William Wootters, now of Williams College in Williamstown, Mass.
Their discovery, Dr. Schumacher believes, may ultimately explain the famous Heisenberg Uncertainty Principle, which has profound ramifications in many areas of physics. That principle, formulated by the German Physicist Werner Heisenberg in 1927, says the position and velocity of a particle cannot be measured simultaneously. More precisely, a particle does not even have a precise position or speed until one or the other is measured.
The uncertainty principle is closely related to one of the main mysteries of quantum physics - the fact that an observation seems to play a role in creating reality. Various features of subatomic particles have no existence until an observation, or measurement, is made. In other words, observations, or measurement, select one of the fuzzy quantum possibilities to become the definite, real outcomes of the classical world.
"It's very processes by which we obtain information about systems...that leads to the classical world of real things that we can look at and handle and touch," said Dr. Caves.
A major problem in quantum mechanics is understanding how measurements generate reality. And a measurement is, in essence, the acquisition of information.
"So the whole notion of information is essential to understanding one of the major problems with the interpretation of quantum mechanics," Dr. Caves said.
Such considerations have led John Wheeler, who has spent decades seeking insight into the meaning of quantum physics, to suggest that understanding information could help illuminate some of the universe's deep mysteries.
"The issues that trouble me, and for which I have no answer, are, How come existence? And how come the quantum?" he said at the Santa Fe meeting.
Dr. Wheeler, of Princeton University, has coined the slogan "it from bit" to suggest that existence itself is constructed from the information acquired in making quantum observations. But he acknowledges that creating existence from observations still requires a way to get observers first.
"One has to hope that one can find reasoning of such a kind to build the whole show from nothing - that would be the dream," he said.
But while quantum information theory promises to open many new avenues for understanding quantum physics, it has not yet solved the primary question of where observers, and existence, come from.
"I'd like to find an idea for explaining the whole show," Dr. Wheeler said at the end of the Santa Fe meeting," and I haven't found it."
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