IN HUMAN relationships, you may never know what your partner is thinking. But
for a pair of quantum particles, even a brief encounter can create a mutual
telepathic bond. Before being measured, both particles are in a fuzzy, undefined
state, yet they still have a special relationship. When the state of one is
measured, the state of the other is instantly defined—even if it is
halfway across the Universe.
In the strange lexicon of quantum physics, the two particles are said to be
“entangled”, a term coined in the 1930s by the German physicist Erwin
Schrödinger. But it’s not just particles—be they electrons or photons
of light—that can be entangled. Different properties of the same particle
can be hitched in this way. Indeed, in theory, entanglement can create an
intimate bond between any quantum systems that have interacted. “Physically it
means that if you perform any kind of measurement on one of the systems it has
an effect on the other even if they are separated by a large distance,” says
Serge Haroche of the École Normale Supérieure in Paris.
For sixty years, entanglement has been at the heart of a philosophical debate
over the nature of the quantum world. But in the past few years there has been a
profound change in the way that physicists view entanglement. It is now an
effect that can be put to work in machines. In the late 1980s, theoreticians
found practical ways to exploit entanglement in entirely new concepts, such as
quantum communication and quantum computing. And just in the past few months,
experimentalists have taken these ideas even further by building devices such as
quantum logic gates, the basic components of quantum computers, and transmitters
that can cram ever larger amounts of information on a single photon.
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Entanglement is probably best known for its role in a famous debate between
Albert Einstein and the Danish physicist Niels Bohr over quantum physics.
Einstein could not cope with the fuzziness of the world predicted by the new
theory. In that world, for example, an electron in an atom has no definite
position, only a range of possible locations, each described by a different
quantum state. At best the theory can give the probability that the electron is
in one of those states. The conventional quantum mechanical view of this
situation is that the electron is not in one place but in all locations at
once—it is in a “superposition” of states. What’s more, it is meaningless
to try to describe the electron’s position until a measurement is made. At that
point, the measurement destroys the superposition and forces the particle to
occupy a definite position.
Einstein disagreed with this interpretation. In his mind, underlying quantum
theory there had to be a world in which a particle’s properties—such as
momentum and position—had real, preexisting values. And in 1935, Einstein
and two colleagues, Boris Podolsky and Nathan Rosen, placed entanglement
centre-stage in a thought experiment designed to show that quantum theory gave
an incomplete view of reality (“The thought that counts”, 51¶ŻÂţ
, 6 May 1995, p 26). They argued that the tie which binds entangled particles
was a physical impossibility because it appeared to act instantaneously, and no
known influence could travel faster than the speed of light. Einstein dubbed it
“spooky action at a distance”.
Bohr saw entanglement as a fact of life. Entangled particles are essential
parts of the same quantum system no matter how far apart they are, he said.
Although no signal passes between them, and no matter how far apart they are,
they do cooperate upon the act of measurement: knowing the quantum state, such
as the position, of one particle tells you the state of the other.
However strange this interpretation may seem, most physicists were happy to
adopt it, although arguments persisted, and still do today. Yet it was not until
1982 that Alain Aspect of the Institute of Optics in Orsay, near Paris, built a
real version of the thought experiment and produced convincing figures to
support Bohr’s view (“The man who proved Einstein wrong”, 51¶ŻÂţ
, 24 November 1990, p 43). Today, researchers are building ever truer versions
of the EPR experiment to probe the boundary between the classical and quantum
worlds.
But something else happened in the 1980s. Theoreticians began to realise that
entanglement could be put to good use beyond understanding quantum theory. Most
of the drive to exploit entanglement sprang from a single idea—quantum
computing. Paul Benioff of Argonne National Laboratory, Illinois, started
investigating the idea of computers that would operate solely at the quantum
level by harnessing entanglement. Charles Bennett of IBM’s Watson Research
Laboratory at Yorktown Heights, New York, and particularly David Deutsch from
the University of Oxford took these ideas further. Then, in 1994, Peter Shor of
AT&T Bell Laboratories in New Jersey caused a stir by presenting the first
algorithm for a quantum computer. It described how such a device would find the
factors of extremely large numbers within seconds. It would be a formidable
tool, capable of cracking even the most secret codes in seconds.
Shor’s paper had a massive impact, says William Wootters, a physicist at
Williams College in Williamstown , Massachusetts. “That was the turning
point—there is no question about it,” he says. “Many people started
working in the field after Peter Shor’s discovery.”
Pumping digits
The building blocks of a conventional computer are logic gates, which carry
out simple operations on the 1s and 0s used in binary machines. A NOT gate, for
example, switches a 1 to a 0 and vice versa. An AND gate, which has two inputs,
sends out a 1 only when both inputs receive a 1: otherwise it sends out a 0.
Conventional computers register 1s or 0s as the presence or absence of electric
current, and their logic gates are made from arrays of transistors. They deal
with complex calculations by pumping digits through a series of different
gates.
The hallmark of a quantum computer, however, is that it would process
superpositions of 1s and 0s. The input data would be converted to superpositions
and processed by quantum logic gates, and the result would emerge as a
superposition of every possible outcome of that computation. “A quantum computer
would in a sense be doing all calculations at the same time,” says Wootters.
Deutsch calls this phenomenon quantum parallelism (“A quantum revolution for
computing”, 51¶ŻÂţ, 24 September 1994, p 21).
There is a snag, however. To read the result there needs to be a
measurement—which would destroy the superposition. Every bit of data would
be forced to occupy a definite quantum state—a 1 or a 0. So any potential
solutions that included the opposite digit—a 0 or a 1—would be lost.
To get round this obstacle, Shor proposed to retrieve his results by allowing
all the components of the final superposition to “interfere” with each other.
Two interfering beams of light, for example, can be used to measure tiny changes
in distance. They produce a pattern of light and dark bands, which changes when
the path length of one beam changes. Shor reckoned that the results of his
quantum computations would emerge in a similar way from his interference
pattern.
Shor’s algorithm is fine in theory, but it cannot be tested because there are
no machines on which it can run. This could be about to change, however. In the
past few months researchers have shown how to build quantum logic gates.
According to H. Jeff Kimble, professor of physics at Caltech, Pasadena, these
devices have emerged partly because of the huge leaps made in controlling the
quantum world. Today, physicists can command lasers to cool atoms, trap
individual atoms or ions, and “tickle” single quantum states of these
particles.
Last December, Kimble and his colleagues described a gate that entangles two
photons. They use a single caesium atom within an optical resonator, a tiny
cavity made of two mirrors that reflect photons back and forth, maximising the
chances that they will interact with the atom’s outer electron. In Caesium this
electron can exist in different energy levels. It jumps between two levels if it
receives a photon with energy equal to the energy difference between them.
Kimble’s group exploits a curious energy transition within caesium that is
sensitive to a photon’s polarisation. Polarisation relates to the direction in
which the photon’s electric field oscillates. A photon is said to be circularly
polarised if its field rotates so that it carves out a helix as the photon moves
forward. The researchers found an electron transition within caesium that
responds only to photons with an electric field that rotates clockwise—not
anticlockwise.
Now think of a photon with an electric field that turns clockwise as a 1, and
anticlockwise as a 0. Kimble’s group fired pairs of these photons into the
cavity and analysed their polarisations on the way out. They found the three
photon pairs 0-0, 0-1 and 1-0 interacted in an unremarkable way. But the pair
1-1 underwent a more surprising change. In quantum physics, particles such as
photons and electrons are described mathematically by a “wavefunction”, which
has peaks and troughs like any other wave. When the pair 1-1 emerged from the
cavity, the phase of their wavefunction—the positions of the peaks and
troughs—had shifted. “Both photons interact with each other via the
medium of the atom,” says Kimble.
Photons can also have electric fields that vibrate only in one plane, known
as horizontal or vertical polarisations. These can be viewed as superpositions
of different states of circularly polarised light—in other words,
superpositions of 0s and 1s. If two of these were sent through the cavity,
the
“1-1 components” of these superpositions would interact to change the
wavefunction’s phase, while all the other interacting components would produce
unremarkable results. The photons leaving the cavity would then be in a complex
super-position of the two original superpositions. They would be entangled.
Gates that take 1s and 0s and use them to change the phase of a wavefunction
in this way may have applications in analogue computing, says Kimble. Most
machines designed to deal with Shar’s algorithm, however, use gates that flip 1s
to 0s and vice versa, as a conventional computer does. This is what Dave
Wineland and his group at the National Institute of Standards and Technology in
Boulder, Colorado, have set out to do. They have built a controlled NOT gate,
which flips a “target” bit from 0 to 1 or vice versa only when a second input,
called the control, receives a 1 (see
Diagram). If the control bit is a
0, then the target’s output stays the same as its input. Like Kimble’s gate,
Wineland’s can also process superpositions of 1s and 0s. “The controlled NOT
gate is the fundamental entangling gate,” says Chris Monroe, a member of the
NIST team.
The NIST team has entangled two quantum systems within the same
object—a positively charged beryllium ion. First, the researchers trap the
ion in a web of electric fields known as a Paul trap. The electric forces push
the ion towards the centre, where it vibrates. They then cool the ion to 1
millikelvin, which robs it of nearly all its motion, and screen out any
interference. The ion’s vibrational energy level provides the control bit. An
ion in the lowest vibrational state is a binary 0. An ion in the next highest
vibrational state is equivalent to a 1.
The target is provided by the outer electron, which can exist in one of two
energy levels, depending on the electron’s “spin”. Spin is a quantum mechanical
term analogous to the angular momentum of a spinning top, and in this case comes
in two values—spin down and spin up. Wineland and his team can switch the
electron between these two states with laser pulses. Hit it once and the
electron jumps to spin up, for example, hit it again and it jumps back down. The
length of the laser pulse is also important. If a time t is needed to
make the electron switch states, then 2t will take it to the other
energy level and back to its original state. Weirder still, ½t will leave the
electron in a superposition of spin-up and spin-down states.
So how does the gate work? Let’s assume the electron is spin down and the
vibrational state is 1. The researchers apply three laser pulses (see
Diagram).
The first lasts for ½t and puts the electron in a superposition of
spin-up and spin-down states. The middle pulse exploits a peculiarity of the
experimental setup. On top of the two spin states, the electron has a third
energy level, and the energy needed to reach it depends on the ion’s vibrational
state. The energy of the middle laser pulse is tuned to make the electron jump
to this third level only if it is in its spin-up state and the ion is in
vibrational state 1—so only this component of the superposition is
affected.FIG-mg20494101.GIF
But there is an added twist. The middle pulse is on for 2t. “It
takes the electron up and all the way back,” says Dawn Meekhof, another member
of the team. When the electron returns, the phase of its wavefunction is shifted
through 180°, she says. A 180° phase shift means that the wave’s peaks are where
the troughs were and vice versa.
Awesome series
The third laser pulse, like the first, lasts for ½t. It completes the
electron’s transition to the spin-up state. So, the gate has flipped the
electron from spin down to spin up—analogous to flipping a 0 to a 1. If
the ion’s vibrational state is 0, the middle pulse has no effect on the
electron. And without the 180° phase change, the electron does not jump to spin
up when hit by the third pulse, but falls back to spin down. This is equivalent
to “0 in, 0 out”. In fact, the NIST team has shown that its gate works in the
same way as a classical controlled NOT gate.
Now imagine an experiment in which the vibrational state starts off in a
superposition of states 0 and 1, and the electron begins in the spin-down state.
As the laser pulses are fired, the ion travels through an awesome series of
superpositions, ending up in the not-too-frightening superposition of
vibrational state 0-spin down, and vibrational state 1-spin up. The vibrational
and spin states are now entangled: if you measure the electron’s spin to be
down, for example, you know the vibrational state is 0.
This result also shows Deutsch’s concept of quantum parallelism in action.
The gate has not just performed one controlled NOT operation, but two. The
target bit has been processed as though the vibrational state (the control bit)
were set at both 0 and 1.
Of course, a functioning computer would need more than a single gate, and
mathematicians would need many inputs to carry out parallel processing. At
present, however, researchers have managed to entangle only two quantum systems.
Both Wineland’s and Kimble’s groups have plans to entangle several quantum
systems at once. But even if these experiments succeed, practical quantum
computation could still be some way off. Haroche says that to factor a number
like 15 would take 20 000 logic gate operations on 20 entangled particles. To
handle the extremely large numbers envisioned by Shor would take many times more
operations and gates. Entangling just three particles would be an “experimental
tour de force”, he says. Monroe also stresses that it’s early days. “We’re just
trying to understand this thing called entanglement,” he says.
Another area in which entanglement can be exploited is quantum communication,
a way to send data more efficiently than by conventional means. Today’s digital
telecommunications are limited to sending one of two bits at a time—a 0 or
a 1. The same holds for an atom that, say, can exist in a low or high energy
state. But in 1993, Bennett and Stephen Wiesner, formerly at Columbia
University, New York, realised that if such a two-state particle is a member of
an entangled pair, it can send up to four different digits—0, 1, 2 and 3.
Using binary, it takes eight bits to transmit one of the 256 characters in the
ASCII computer code. But for an entangled particle capable of conveying one of
four digits, the same job could be done with four particles.
In June, Harald Weinfurter at the University of Innsbruck in Austria and his
team published results showing that they had moved part way towards this goal by
encoding one of three digits—or trits, as they call them—onto a
single entangled photon (Science, 51¶ŻÂţ, 6 July, p 16). They
sent an ASCII character using 5 trits instead of 8 bits.
Weinfurter’s team generate the entanglement by passing a single ultraviolet
photon through a material called beta barium borate, which splits single photons
into two photons, one polarised horizontally, the other vertically. These
photons are entangled because it is impossible to tell which is polarised
horizontally and which vertically, until a measurement is made.
One photon passes through an encoder where it undergoes one of four
operations, each of which represents a digit. The photon may have its
polarisation flipped or its phase changed, or a combination of the two; or it
may be left alone. The two photons are recombined and sent to the recipient, who
has an array of detectors (see
Diagram).
The group analyses how each entangled photon interferes with its partner to
reveal the encoding added at the transmitter, and hence the digit it carries.
Although Weinfurter used four distinct changes to encode his signal, two of them
appeared the same to the detectors. This meant he could only assign one of only
three digits to each photon.
Quantum communication is still in its infancy, so it’s likely to be many
years before the phone company starts sending entangled pairs down its fibre
optic cables. The potential, however, is enormous, says Wootters, because it is
possible to cram even more than four digits on an entangled particle. If the
quantum system has three distinct states, you can theoretically encode up to
nine different messages.
But once again, the spanner in the works is how to entangle more than two
quantum systems. Many physicists remain sceptical about the prospects of such
schemes. Haroche feels that entanglement will always be on a small
scale—perhaps no more than a few dozen entangled systems. Entanglement is
extremely fragile, says Haroche. Disturbing one member of an entangled pair will
destroy any superposition. Making a measurement is one way to do this, but
“noise” is more insidious. Tiny movements of an ion in an electric field trap,
for example, induce currents in the trap’s electrodes which draw energy from the
ion and destroy any entanglement. This “decoherence” is the arch enemy of
entanglement and is eventually inevitable. And if you tried to entangle 10
photons, “you will have to look for the entanglement 10 times faster” before
decoherence sets in, says Haroche.
But other physicists believe decoherence can be defeated by quantum error
correction. Just as in conventional error correction, this means storing the
same bit of information in several places. Entangling these redundant bits would
allow researchers to detect if any had become corrupted. IBM physicist David
DiVincenzo is optimistic that quantum error correction can defeat decoherence.
“We have been accustomed to say that entangled states are very delicate and fall
apart very easily,” he says. “But in the setting of quantum computation, I
believe that we will say that the opposite is true. Entangled states can be made
very robust.”
If he is right, we may see quantum computers and quantum communications in
the next few years. Whatever the outcome, it seems ironic that entanglement,
which Einstein chose as a way to undermine quantum mechanics, today underpins a
vast new field of research.
- References and further reading for this article are available on Planet
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