The Information

by James Gleick

  This imperfect distinguishability is what gives quantum physics its dreamlike character: the inability to observe systems without disturbing them; the inability to clone quantum objects or broadcast them to many listeners. The qubit has this dreamlike character, too. It is not just either-or. Its 0 and 1 values are represented by quantum states that can be reliably distinguished—for example, horizontal and vertical polarizations—but coexisting with these are the whole continuum of intermediate states, such as diagonal polarizations, that lean toward 0 or 1 with different probabilities. So a physicist says that a qubit is a superposition of states; a combination of probability amplitudes. It is a determinate thing with a cloud of indeterminacy living inside. But the qubit is not a muddle; a superposition is not a hodgepodge but a combining of probabilistic elements according to clear and elegant mathematical rules.

  “A nonrandom whole can have random parts,” says Bennett. “This is the most counterintuitive part of quantum mechanics, yet it follows from the superposition principle and is the way nature works, as far as we know. People may not like it at first, but after a while you get used to it, and the alternatives are far worse.”

  The key to teleportation and to so much of the quantum information science that followed is the phenomenon known as entanglement. Entanglement takes the superposition principle and extends it across space, to a pair of qubits far apart from each other. They have a definite state as a pair even while neither has a measurable state on its own. Before entanglement could be discovered, it had to be invented, in this case by Einstein. Then it had to be named, not by Einstein but by Schrödinger. Einstein invented it for a thought experiment designed to illuminate what he considered flaws in quantum mechanics as it stood in 1935. He publicized it in a famous paper with Boris Podolsky and Nathan Rosen titled “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?”♦ It was famous in part for provoking Wolfgang Pauli to write to Werner Heisenberg, “Einstein has once again expressed himself publicly on quantum mechanics.… As is well known, this is a catastrophe every time it happens.”♦ The thought experiment imagined a pair of particles correlated in a special way, as when, for example, a pair of photons are emitted by a single atom. Their polarization is random but identical—now and as long as they last.

  THE QUBIT

  Einstein, Podolsky, and Rosen investigated what would happen when the photons are far apart and a measurement is performed on one of them. In the case of entangled particles—the pair of photons, created together and now light-years apart—it seems that the measurement performed on one has an effect on the other. The instant Alice measures the vertical polarization of her photon, Bob’s photon will also have a definite polarization state on that axis, whereas its diagonal polarization will be indefinite. The measurement thus creates an influence apparently traveling faster than light. It seemed a paradox, and Einstein abhorred it. “That which really exists in B should not depend on what kind of measurement is carried out in space A,”♦ he wrote. The paper concluded sternly, “No reasonable definition of reality could be expected to permit this.” He gave it the indelible name spukhafte Fernwirkung, “spooky action at a distance.”

  In 2003 the Israeli physicist Asher Peres proposed one answer to the Einstein-Podolsky-Rosen (EPR) puzzle. The paper was not exactly wrong, he said, but it had been written too soon: before Shannon published his theory of information, “and it took many more years before the latter was included in the physicist’s toolbox.”♦ Information is physical. It is no use talking about quantum states without considering the information about the quantum states.

  Information is not just an abstract notion. It requires a physical carrier, and the latter is (approximately) localized. After all, it was the business of the Bell Telephone Company to transport information from one telephone to another telephone, in a different location.

  … When Alice measures her spin, the information she gets is localized at her position, and will remain so until she decides to broadcast it. Absolutely nothing happens at Bob’s location.… It is only if and when Alice informs Bob of the result she got (by mail, telephone, radio, or by means of any other material carrier, which is naturally restricted to the speed of light) that Bob realizes that his particle has a definite pure state.

  For that matter, Christopher Fuchs argues that it is no use talking about quantum states at all. The quantum state is a construct of the observer—from which many troubles spring. Exit states; enter information. “Terminology can say it all: A practitioner in this field, whether she has ever thought an ounce about quantum foundations, is just as likely to say ‘quantum information’ as ‘quantum state’…‘What does the quantum teleportation protocol do?’ A now completely standard answer would be: ‘It transfers quantum information from Alice’s site to Bob’s.’ What we have here is a change of mind-set.”♦

  The puzzle of spooky action at a distance has not been altogether resolved. Nonlocality has been demonstrated in a variety of clever experiments all descended from the EPR thought experiment. Entanglement turns out to be not only real but ubiquitous. The atom pair in every hydrogen molecule, H2, is quantumly entangled (“verschränkt,” as Schrödinger said). Bennett put entanglement to work in quantum teleportation, presented publicly for the first time in 1993.♦ Teleportation uses an entangled pair to project quantum information from a third particle across an arbitrary distance. Alice cannot measure this third particle directly; rather, she measures something about its relation to one of the entangled particles. Even though Alice herself remains ignorant about the original, because of the uncertainty principle, Bob is able to receive an exact replica. Alice’s object is disembodied in the process. Communication is not faster than light, because Alice must also send Bob a classical (nonquantum) message on the side. “The net result of teleportation is completely prosaic: the removal of [the quantum object] from Alice’s hands and its appearance in Bob’s hands a suitable time later,” wrote Bennett and his colleagues. “The only remarkable feature is that in the interim, the information has been cleanly separated into classical and nonclassical parts.”

  Researchers quickly imagined many applications, such as transfer of volatile information into secure storage, or memory. With or without goulash, teleportation created excitement, because it opened up new possibilities for the very real but still elusive dream of quantum computing.

  The idea of a quantum computer is strange. Richard Feynman chose the strangeness as his starting point in 1981, speaking at MIT, when he first explored the possibility of using a quantum system to compute hard quantum problems. He began with a supposedly naughty digression—“Secret! Secret! Close the doors …”♦

  We have always had a great deal of difficulty in understanding the world view that quantum mechanics represents. At least I do, because I’m an old enough man [he was sixty-two] that I haven’t got to the point that this stuff is obvious to me. Okay, I still get nervous with it.… It has not yet become obvious to me that there is no real problem. I cannot define the real problem, therefore I suspect there’s no real problem, but I’m not sure there’s no real problem.

  He knew very well what the problem was for computation—for simulating quantum physics with a computer. The problem was probability. Every quantum variable involved probabilities, and that made the difficulty of computation grow exponentially. “The number of information bits is the same as the number of points in space, and therefore you’d have to have something like NN configurations to be described to get the probability out, and that’s too big for our computer to hold.… It is therefore impossible, according to the rules stated, to simulate by calculating the probability.”

  So he proposed fighting fire with fire. “The other way to simulate a probabilistic Nature, which I’ll call N for the moment, might still be to simulate the probabilistic Nature by a computer C which itself is probabilistic.” A quantum computer would not be a Turing machine, he said. It would be something altogether new.

  “Fe
ynman’s insight,” says Bennett, “was that a quantum system is, in a sense, computing its own future all the time. You may say it’s an analog computer of its own dynamics.”♦ Researchers quickly realized that if a quantum computer had special powers in cutting through problems in simulating physics, it might be able to solve other types of intractable problems as well.

  The power comes from that shimmering, untouchable object the qubit. The probabilities are built in. Embodying a superposition of states gives the qubit more power than the classical bit, always in only one state or the other, zero or one, “a pretty miserable specimen of a two-dimensional vector,”♦ as David Mermin says. “When we learned to count on our sticky little classical fingers, we were misled,” Rolf Landauer said dryly. “We thought that an integer had to have a particular and unique value.” But no—not in the real world, which is to say the quantum world.

  In quantum computing, multiple qubits are entangled. Putting qubits at work together does not merely multiply their power; the power increases exponentially. In classical computing, where a bit is either-or, n bits can encode any one of 2n values. Qubits can encode these Boolean values along with all their possible superpositions. This gives a quantum computer a potential for parallel processing that has no classical equivalent. So quantum computers—in theory—can solve certain classes of problems that had otherwise been considered computationally infeasible.

  An example is finding the prime factors of very large numbers. This happens to be the key to cracking the most widespread cryptographic algorithms in use today, particularly RSA encryption.♦ The world’s Internet commerce depends on it. In effect, the very large number is a public key used to encrypt a message; if eavesdroppers can figure out its prime factors (also large), they can decipher the message. But whereas multiplying a pair of large prime numbers is easy, the inverse is exceedingly difficult. The procedure is an informational one-way street. So factoring RSA numbers has been an ongoing challenge for classical computing. In December 2009 a team distributed in Lausanne, Amsterdam, Tokyo, Paris, Bonn, and Redmond, Washington, used many hundreds of machines working almost two years to discover that 1230186684530117755130494958384962720772853569595334792197322452151726400507263657518745202199786469389956474942774063845925192557326303453731548268507917026122142913461670429214311602221240479274737794080665351419597459856902143413 is the product of 33478071698956898786044169848212690817704794983713768568912431388982883793878002287614711652531743087737814467999489 and 36746043666799590428244633799627952632279158164343087642676032283815739666511279233373417143396810270092798736308917. They estimated that the computation used more than 1020 operations.♦

  This was one of the smaller RSA numbers, but, had the solution come earlier, the team could have won a $50,000 prize offered by RSA Laboratories. As far as classical computing is concerned, such encryption is considered quite secure. Larger numbers take exponentially longer time, and at some point the time exceeds the age of the universe.

  Quantum computing is another matter. The ability of a quantum computer to occupy many states at once opens new vistas. In 1994, before anyone knew how actually to build any sort of quantum computer, a mathematician at Bell Labs figured out how to program one to solve the factoring problem. He was Peter Shor, a problem-solving prodigy who made an early mark in math olympiads and prize competitions. His ingenious algorithm, which broke the field wide open, is known by him simply as the factoring algorithm, and by everyone else as Shor’s algorithm. Two years later Lov Grover, also at Bell Labs, came up with a quantum algorithm for searching a vast unsorted database. That is the canonical hard problem for a world of limitless information—needles and haystacks.

  “Quantum computers were basically a revolution,”♦ Dorit Aharonov of Hebrew University told an audience in 2009. “The revolution was launched into the air by Shor’s algorithm. But the reason for the revolution—other than the amazing practical implications—is that they redefine what is an easy and what is a hard problem.”

  What gives quantum computers their power also makes them exceedingly difficult to work with. Extracting information from a system means observing it, and observing a system means interfering with the quantum magic. Qubits cannot be watched as they do their exponentially many operations in parallel; measuring that shadow-mesh of possibilities reduces it to a classical bit. Quantum information is fragile. The only way to learn the result of a computation is to wait until after the quantum work is done.

  Quantum information is like a dream—evanescent, never quite existing as firmly as a word on a printed page. “Many people can read a book and get the same message,” Bennett says, “but trying to tell people about your dream changes your memory of it, so that eventually you forget the dream and remember only what you said about it.”♦ Quantum erasure, in turn, amounts to a true undoing: “One can fairly say that even God has forgotten.”

  As for Shannon himself, he was unable to witness this flowering of the seeds he had planted. “If Shannon were around now, I would say he would be very enthusiastic about the entanglement-assisted capacity of a channel,”♦ says Bennett. “The same form, a generalization of Shannon’s formula, covers both classic and quantum channels in a very elegant way. So it’s pretty well established that the quantum generalization of classical information has led to a cleaner and more powerful theory, both of computing and communication.” Shannon lived till 2001, his last years dimmed and isolated by the disease of erasure, Alzheimer’s. His life had spanned the twentieth century and helped to define it. As much as any one person, he was the progenitor of the information age. Cyberspace is in part his creation; he never knew it, though he told his last interviewer, in 1987, that he was investigating the idea of mirrored rooms: “to work out all the possible mirrored rooms that make sense, in that if you looked everywhere from inside one, space would be divided into a bunch of rooms, and you would be in each room and this would go on to infinity without contradiction.”♦ He hoped to build a gallery of mirrors in his house near MIT, but he never did.

  It was John Wheeler who left behind an agenda for quantum information science—a modest to-do list for the next generation of physicists and computer scientists together:♦

  “Translate the quantum versions of string theory and of Einstein’s geometrodynamics from the language of continuum to the language of bit,” he exhorted his heirs.

  “Survey one by one with an imaginative eye the powerful tools that mathematics—including mathematical logic—has won … and for each such technique work out the transcription into the world of bits.”

  And, “From the wheels-upon-wheels-upon-wheels evolution of computer programming dig out, systematize and display every feature that illuminates the level-upon-level-upon-level structure of physics.”

  And, “Finally. Deplore? No, celebrate the absence of a clean clear definition of the term ‘bit’ as elementary unit in the establishment of meaning.… If and when we learn how to combine bits in fantastically large numbers to obtain what we call existence, we will know better what we mean both by bit and by existence.”

  This is the challenge that remains, and not just for scientists: the establishment of meaning.

  * * *

  ♦ “It was either R4 or a black hole. But the Feynman sum over histories allows it to be both at once.”

  ♦ Von Neumann’s formula for the theoretical energy cost of every logical operation was kT ln 2 joules per bit, where T is the computer’s operating temperature and k is the Boltzman constant. Szilárd had proved that the demon in his engine can get kT ln 2 of work out of every molecule it selects, so that energy cost must be paid somewhere in the cycle.

  ♦ This word is not universally accepted, though the OED recognized it as of December 2007. David Mermin wrote that same year: “Unfortunately the preposterous spelling qubit currently holds sway.… Although “qubit” honors the English (German, Italian,…) rule that q should be followed by u, it ignores the equally powerful requirement that qu should be followed by a vowel. My gue
ss is that “qubit” has gained acceptance because it visually resembles an obsolete English unit of distance, the homonymic cubit. To see its ungainliness with fresh eyes, it suffices to imagine … that one erased transparencies and cleaned ones ears with Qutips.”

  14 | AFTER THE FLOOD

  (A Great Album of Babel)

  Suppose within every book there is another book, and within every letter on every page another volume constantly unfolding; but these volumes take no space on the desk. Suppose knowledge could be reduced to a quintessence, held within a picture, a sign, held within a place which is no place.

  —Hilary Mantel (2009)♦

  “THE UNIVERSE (which others call the Library)…”♦

  Thus Jorge Luis Borges began his 1941 story “The Library of Babel,” about the mythical library that contains all books, in all languages, books of apology and prophecy, the gospel and the commentary upon that gospel and the commentary upon the commentary upon the gospel, the minutely detailed history of the future, the interpolations of all books in all other books, the faithful catalogue of the library and the innumerable false catalogues. This library (which others call the universe) enshrines all the information. Yet no knowledge can be discovered there, precisely because all knowledge is there, shelved side by side with all falsehood. In the mirrored galleries, on the countless shelves, can be found everything and nothing. There can be no more perfect case of information glut.