The Information (63 page)

In the real world of 1970s computing, hardware had rapidly grown thousands of times more energy-efficient than during the early vacuum-tube era. Nonetheless, electronic computers dissipate considerable energy in the form of waste heat. The closer they come to their theoretical minimum of energy use, the more urgently scientists want to know
just what that theoretical minimum is. Von Neumann, working with his big computers, made a back-of-the-envelope calculation as early as 1949, proposing an amount of heat that must be dissipated “per elementary act of information, that is per elementary decision of a two-way alternative and per elementary transmittal of one unit of information.”
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He based it on the molecular work done in a model thermodynamic system by Maxwell’s demon, as reimagined by Leó Szilárd.
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Von Neumann said the price is paid by every elementary act of information processing, every choice between two alternatives. By the 1970s this was generally accepted. But it was wrong.

Von Neumann’s error was discovered by the scientist who became Bennett’s mentor at IBM, Rolf Landauer, an exile from Nazi Germany.
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Landauer devoted his career to establishing the physical basis of information. “Information Is Physical” was the title of one famous paper, meant to remind the community that computation requires physical objects and obeys the laws of physics. Lest anyone forget, he titled a later essay—his last, it turned out—“Information Is Inevitably Physical.” Whether a bit is a mark on a stone tablet or a hole in a punched card or a particle with spin up or down, he insisted that it could not exist without
some
embodiment. Landauer tried in 1961 to prove von Neumann’s formula for the cost of information processing and discovered that he could not. On the contrary, it seemed that most logical operations have no entropy cost at all. When a bit flips from zero to one, or vice-versa, the information is preserved. The process is reversible. Entropy is unchanged; no heat needs to be dissipated. Only an irreversible operation, he argued, increases entropy.

Landauer and Bennett were a double act: a straight and narrow old IBM type and a scruffy hippie (in Bennett’s view, anyway).
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The younger man pursued Landauer’s principle by analyzing every kind of computer he could imagine, real and abstract, from Turing machines and
messenger RNA to “ballistic” computers, carrying signals via something like billiard balls. He confirmed that a great deal of computation can be done with no energy cost at all. In every case, Bennett found, heat dissipation occurs only when information is
erased
. Erasure is the irreversible logical operation. When the head on a Turing machine erases one square of the tape, or when an electronic computer clears a capacitor, a bit is lost, and
then
heat must be dissipated. In Szilárd’s thought experiment, the demon does not incur an entropy cost when it observes or chooses a molecule. The payback comes at the moment of clearing the record, when the demon erases one observation to make room for the next.

Forgetting takes work.

“You might say this is the revenge of information theory on quantum mechanics,”
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Bennett says. Sometimes a successful idea in one field can impede progress in another. In this case the successful idea was the uncertainty principle, which brought home the central role played by the measurement process itself. One can no longer talk simply about “looking” at a molecule; the observer needs to employ photons, and the photons must be more energetic than the thermal background, and complications ensue. In quantum mechanics the act of observation has consequences of its own, whether performed by a laboratory scientist or by Maxwell’s demon. Nature is sensitive to our experiments.

“The quantum theory of radiation helped people come to the incorrect conclusion that computing had an irreducible thermodynamic cost per step,” Bennett says. “In the other case, the success of Shannon’s theory of information processing led people to abstract away all of the physics from information processing and think of it as a totally mathematical thing.” As communications engineers and chip designers came closer and closer to atomic levels, they worried increasingly about quantum limitations interfering with their clean, classical ability to distinguish zero and one states. But now they looked again—and this, finally, is where quantum information science is born. Bennett and others began
to think differently: that quantum effects, rather than being a nuisance, might be turned to advantage.

Wedged like a hope chest against a wall of his office at IBM’s research laboratory in the wooded hills of Westchester is a light-sealed device called Aunt Martha (short for Aunt Martha’s coffin). Bennett and his research assistant John Smolin jury-rigged it in 1988 and 1989 with a little help from the machine shop: an aluminum box spray-painted dull black on the inside and further sealed with rubber stoppers and black velvet.
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With a helium-neon laser for alignment and high-voltage cells to polarize the photons, they sent the first message ever to be encoded by quantum cryptography. It was a demonstration of an information-processing task that could be effectively accomplished only via a quantum system. Quantum error correction, quantum teleportation, and quantum computers followed shortly behind.

The quantum message passed between Alice and Bob, a ubiquitous mythical pair. Alice and Bob got their start in cryptography, but the quantum people own them now. Occasionally they are joined by Charlie. They are constantly walking into different rooms and flipping quarters and sending each other sealed envelopes. They choose states and perform Pauli rotations. “We say things such as ‘Alice sends Bob a qubit and forgets what she did,’ ‘Bob does a measurement and tells Alice,’”
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explains Barbara Terhal, a colleague of Bennett’s and one of the next generation of quantum information theorists. Terhal herself has investigated whether Alice and Bob are
monogamous
—another term of art, naturally.

In the Aunt Martha experiment, Alice sends information to Bob, encrypted so that it cannot be read by a malevolent third party (Eve the eavesdropper). If they both know their private key, Bob can decipher the message. But how is Alice to send Bob the key in the first place? Bennett and Gilles Brassard, a computer scientist in Montreal, began by encoding each bit of information as a single quantum object, such as a photon. The information resides in the photon’s quantum states—for example, its horizontal or vertical polarization. Whereas an object in classical physics, typically composed of billions of particles, can be intercepted,
monitored, observed, and passed along, a quantum object cannot. Nor can it be copied or cloned. The act of observation inevitably disrupts the message. No matter how delicately eavesdroppers try to listen in, they can be detected. Following an intricate and complex protocol worked out by Bennett and Brassard, Alice generates a sequence of random bits to use as the key, and Bob is able to establish an identical sequence at his end of the line.
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The first experiments with Aunt Martha’s coffin managed to send quantum bits across thirty-two centimeters of free air. It was not
Mr. Watson, come here, I want to see you
, but it was a first in the history of cryptography: an absolutely unbreakable cryptographic key. Later experimenters moved on to optical fiber. Bennett, meanwhile, moved on to quantum teleportation.

He regretted that name soon enough, when the IBM marketing department featured his work in an advertisement with the line “Stand by: I’ll teleport you some goulash.”
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But the name stuck, because teleportation worked. Alice does not send goulash; she sends qubits.
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♦

The qubit is the smallest nontrivial quantum system. Like a classical bit, a qubit has two possible values, zero or one—which is to say, two states that can be reliably distinguished. In a classical system,
all
states are distinguishable in principle. (If you cannot tell one color from another, you merely have an imperfect measuring device.) But in a quantum system, imperfect distinguishability is everywhere, thanks to Heisenberg’s uncertainty principle. When you measure any property of a quantum object, you thereby lose the ability to measure a complementary property. You can discover a particle’s momentum or its position but not both. Other complementary properties include directions of spin and,
as in Aunt Martha’s coffin, polarization. Physicists think of these quantum states in a geometrical way—the states of a system corresponding to directions in space (a space of many possible dimensions), and their distinguishability depending on whether those directions are perpendicular (or “orthogonal”).

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?”
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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.”
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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.

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,”
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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.”
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Information is physical. It is no use talking about quantum states without considering the
information
about the quantum states.