WHAT does a financial index have in common with Shakespeare鈥檚 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. 鈥淚nformation is deeper
than reality,鈥� says Anton Zeilinger, a physicist at the University of
Innsbruck.
Zeilinger鈥檚 shattering insight comes after years of studying information in
the quantum world鈥攐ne 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鈥檚 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.
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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鈥檛 so sure. Could it be the other way round? Quantum particles might be
catching their behaviour from the information they contain. 鈥淏y thinking this
way,鈥� says Zeilinger, 鈥渨e get a deeper grasp of quantum physics. And we begin to
see that quantum theory is more than a theory of physics鈥攊t鈥檚 a theory of
颈苍蹿辞谤尘补迟颈辞苍.鈥�
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鈥攊t can spin clockwise or
anti-clockwise about the direction of the field. Physicists call these states
鈥渦p鈥� or 鈥渄own鈥� because the electron鈥檚 spin makes it act like a tiny upward or
downward pointing magnet. Call one of these states 鈥�0鈥� and the other 鈥�1鈥�, and an
electron鈥檚 spin naturally stores one bit.
A two-state quantum system like this is called a 鈥渜ubit,鈥� and doesn鈥檛 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鈥檛. A quantum particle can split its existence and enter into a
鈥渟uperposition鈥� 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 鈥渆ntangled state鈥�, 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).
鈥淚n an entangled state,鈥� says Charles Bennett of the IBM Research
Division in Yorktown Heights, New York, 鈥渄istant particles are linked in a way
that they classically couldn鈥檛 be unless they were in the same place.鈥� 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鈥� 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鈥攁 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鈥攎easuring the exact state of a quantum system. 鈥淵ou can鈥檛 make copies
of quantum information,鈥� says Bennett. Why? Because if you measure an electron鈥檚
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鈥檛
know what the electron鈥檚 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鈥攁
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鈥攜ou just can鈥檛 know what it is
you鈥檙e sending. Zeilinger and his colleagues at Innsbruck have now put Bennett鈥檚
ideas into practice, and are routinely teleporting single photons around their
lab.
Weird link
In Bennett鈥檚 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 鈥渕essage鈥� 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鈥檚 spot, even though
C never really moves physically.
You can鈥檛 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鈥檚 idea is to use entanglement to recapture the disappearing portion
of the quantum information. 鈥淚t is resource for communication,鈥� he says. For the
entangled pair A and B can be used as a tool to move C鈥檚 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鈥檚 identical to
the original C. This is the trick that Zeilinger鈥檚 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鈥攂y
teleporting all of their particles鈥攖hen 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鈥攊n a
process known as 鈥渄ecoherence鈥濃�攊f 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鈥� 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鈥�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鈥檚 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鈥攕uch as telephone directories or
huge databases鈥攆ar more effectively than classical computers.
Like teleportation, quantum computing has only been done so far with two qubits
(see 鈥淲ake up to quantum coffee鈥�, New 杏吧原创, 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. 鈥淚鈥檓 most sceptical of computing,鈥� says
Rolf Landauer, another IBM researcher, 鈥渂ecause quantum parallelism is the most
demanding of these things.鈥�
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. 鈥淚鈥檓 convinced that we will have a new
information technology in the future, and that it will use quantum technology,鈥�
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鈥檛 be fatal. By encoding the information in
鈥渆rror-correcting codes鈥�, additional operations in the computer can be made to counter
any mistakes, and repair their damage. 鈥淓rror correction achieves the apparently
impossible,鈥� says Steane, 鈥渟ince a computation can preserve quantum coherence
even though during its course every qubit in the computer will have relaxed many
迟颈尘别蝉.鈥�
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鈥檛 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 鈥渇ault tolerant鈥�, 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 鈥渢he amount of entanglement in a maximally
entangled pair鈥�. They called it an ebit鈥攁 single 鈥減article鈥� of
entanglement. Thinking of qubits and ebits as 鈥減articles鈥� 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 鈥渧irtual鈥� 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鈥檚 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 鈥渧irtual鈥� information. In traditional
information theory, information is always real鈥攋ust 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鈥攁 qubit and an anti-qubit鈥攐ut 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鈥攖he 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. 鈥淚nformation is such a fundamental thing,鈥� says Steane. 鈥淭he
ambitious goal is to discover its basic properties, and then from that deduce
quantum theory.鈥�
There鈥檚 no telling where this kind of thinking will lead.