ISIS Press Release 22/03/04
The Quantum Information Revolution
Quantum information processing takes advantage of some strange
properties of the quantum world that have been known for more than a century.
Dr. Mae-Wan Ho unravels some of the
mysteries
A more technical version of this article with sources is posted on ISIS members’ website. Details here.
In 1948, Claude Shannon discovered how to quantify information as binary
‘bits’ – a ‘1’ or ‘0’ – which can
represent any number, or combinations of logical operations. This started the
‘information technology revolution’ that has lasted close to fifty
years, with exponential growth in computing power, referred to as
‘Moore’s Law’: the doubling in the number of components
representing bits that can be packed on a chip every year or two. But
Moore’s Law is rapidly approaching its limits as bits are now shrunk to
the size of molecules in the emerging field of molecular electronics (see
"Nanotubes highly toxic", SiS 21). Does that
mean computing power will have reached its limit or can there be a totally
different approach that could allow us to jump over that barrier to much
faster, more powerful and infinitely more efficient computing?
The answer for the moment is a very excited yes possibly, by means of a
literal quantum leap to quantum information processing, taking advantage of the
properties of superposition and entanglement of quantum systems
(see "How not to collapse the wave function", this series, for
definitions).
Thus, photons, electrons or qubits (see below) that have interacted
with each other, retain an exquisite organic connection. So, measuring the spin
state of one entangled particle, for example, allows one to know that the spin
state of the other is exactly in the opposite direction. Moreover, on account
of quantum superposition, neither the measured particle, nor its entangled
partner has a single spin direction before being measured, but is
simultaneously both spin-up and spin-down. Quantum entanglement allows qubits
that are separated by great distances to interact instantaneously (or
nonlocally).
Entanglement has been demonstrated repeatedly in experiments, and is
currently being exploited for quantum cryptography and quantum computing.
Quantum computing
For a quantum system, the fundamental unit of information is a quantum
bit, or ‘qubit’ (see "Quantum computer, is it alive?" ISIS News 2001,
11/12). Qubits can
be represented by alternative states of a photon’s polarisation, or an
electron’s spin, and can be prepared in a coherent superposition of states
of 1 and 0:
׀ψ›
= a?0› + b?1›
(1)
Here, a and b are
the ‘complex quantum amplitudes’ (expressed in complex numbers) which
when squared, gives the classical probabilities, upon measurement, of finding
the system in a ׀0› or a ׀1› state. This is only one bit of information, but because
the amplitudes are continuous, they carry an infinite amount of information,
similar to analogue information carriers such as the continuous voltage stored
on capacitors.
Quantum bits offer much more also on account of quantum entanglement. In
a classical analogue system, one needs N capacitors to store N continuous
voltages. But a quantum system with N qubits, in the most general case, is a
superposition of 2N states each with its own quantum amplitude.
A collection of qubits can therefore store exponentially more
information than a comparable collection of classical information carriers. All
the N qubits in the system are entangled or inseparable. It is this
entanglement that give quantum computing its power, at least in principle.
Quantum information processing requires qubits to behave as quantum
memories for long-term storage, and for many applications to behave as quantum
transmitters for long-distance communication. It was thought that cold and
localized individual atoms are the natural choice for qubit memories and
sources of local enanglement for quantum information processing, while
individual photons are the natural choice for communication of quantum
information, as they can travel large distances through the atmosphere or
optical fibres with minimal disturbance.
But whether an actual quantum computer can be built is very much
debated. There are many obstacles to overcome, a major one being the loss of
quantum coherence, which would destroy quantum superposition and quantum
entanglement that quantum computing depends on; and the larger the number of
qubits involved, the bigger the problem. Apart from these engineering problems
of implementation that have been mentioned, could there be a deeper problem
that a quantum computer is like an organism, and shares with it the important
property that as such, it is radically incontrollable and hence unable to serve
our instrumental purposes (see "Quantum computer, is it alive?"
ISIS News
2001, 11/12 )?
Quantum communication and quantum crytography
Imagine that two parties, A and B, or Alice and Bob, share two entangled
qubits, say a pair of photons, that are perfectly correlated, so the photons
can both only be in the 0, or in the 1 state.
Before Alice or Bob measures her or his photon, the entangled pair of
photons is in a superposition of the two (classically) mutually exclusive
states. But as soon as either does a measurement, the state of the other photon
will be instantaneously determined. The entangled pair has equal probability of
being measured 0 or 1. According to classical information theory, a string of
random 0 and 1 carries no information. But, correlated random strings are just
the crytographer’s dream, as they provide the one-off key for decoding
information that can be changed with each message.
Quantum crytography was first described in 1984 by theoretical
physicists Charles Bennett of IBM’s Thomas J. Watson Research Centre in
Yorktown Heights, Hew York and Gilles Brassard of the University of Montreal in
Canada. And it goes like this.
Supposing Alice and Bob share a series of entangled photons. Alice and
Bob agree beforehand that a horizontal polarization corresponds to a
‘0’ and a vertical polarization to a ‘1’, and make a
similar decision for the two diagonal polarizations, left or right. And suppose
that Alice does the measurement before Bob.
Now, Bob can either look to see whether the photon he receives, after
Alice has measured its entangled twin, is horizontally or vertically polarised
by performing one measurement, or he can see whether it is left or right
polarized by performing another measurement, but he cannot do both. So when the
photon arrives at Bob’s, he randomly chooses to do the up-down measurement
or the left-right (diagonal) measurement. If Bob makes a diagonal measurement,
the photon lies exactly midway between vertical or horizontal. And if Alice has
made the measurement for up-down polarization, then there is fifty-fifty chance
for Bob’s photon to be left or right polarised.
At the end of the transmission of all the photons, Bob will know he
has, by random chance, correctly measured the polarizations of about half of
all the photons, but doesn’t know which ones. Bob contacts Alice on a
channel that does not have to be secure, say, by telephone, and tells her which
type of measurement he has made for each photon. Alice replies to tell Bob
which measurements were correct (the same as the ones she made). They discard
the discordant ones and keep the rest for their key.
To make sure that an eavesdropper, Eve, isn’t listening, Alice and
Bob sacrifice a small number of their key to check it over the public channel
for errors. If Eve has been snooping, and assessing the polarisation of the
photons passing between Alice and Bob, she will have changed the polarisation
of about half of them. Alice and Bob will notice this immediately.
That is the ideal scenario. In practice, the distance that the
entangled photons that make up the key can be transmitted is more of a problem.
For example, noise in the channel through which the photons pass will introduce
a small number of errors, so a clever eavesdropper will measure such a small
number of photons that Alice and Bob will not be able to tell whether the
discrepancy is due to errors or eavesdropping. Though, under such
circumstances, Alice and Bob can generate a new key by simply applying an
algorithm to their existing key. So Eve, who is missing the bulk of the
original key, cannot hope to predict the outcome of the algorithm.
There is yet another complication. It is possible for Eve to carry out
‘weak’ measurements that will not change the polarisation of the
photons she is snooping on (see "How not to collapse the wave function" this
series).
In 1989, a team led by Bennett and Brassard built a working device, and
sent photons through the air to a receiver about 30 centimetres away. By the
mid-1990s, other groups were sending encrypted keys through tens of kilometres
of optical fibre.
In October 2001, a team of physicists at the University of Geneva in
Switzerland launched a company called id Quantique, which will supply a system
integrating the crytography hardware – photon sources and detectors, and
fibre-optic connections – needed to exchange keys. In March 2002, they
used the system to send single photons through 67 km telecommunication cables
running under Lake Geneva. " The system is very stable, and has the potential
to be very fast." Said Nicolas Gisin, a member of the team.
MagiQ Technologies, a New York firm that specializes in quantum
technologies, is building another system, that like id Quantique, connects
users linked by a single dedicated fibre. Other groups are working on systems
that can support a network of users. In September 2001, BBN Technologies, based
in Cambridge, Massachusettes began a five-year collaboration with teams at
Boston and Harvard univerties to build a quantum network connecting the three
institutions. Photons will be routed round the network using mirrors, "which
send the photons along without measuring them".
Another problem is that reliable single photon generators are not yet
commercially available. Today’s system, such as those developed by id
Quantique, use lasers that generate pulses so weak that they almost never
contain more than one photon. But at such low intensities, nine out of ten
attempts to fire a photon fail.
Photon detection is also difficult. To spot a single photon, the
detectors must be so sensitive that they will sometimes register photons that
are not there. Even then, they will typically miss 90% of all the transmitted
photons. What’s more, many photons are absorbed by the optical fibre and
never make it to receiver. Out of some 5 million bits per second sent,
somewhere between 100 and 1 000 bits per second is received. But even this is
enough for cryptography.
The Advanced Encryption Standard, the encryption algorithm used by the
US government, uses a key with a maximum of 256 bits. A key distribution that
send 500 bits per second would allow users to change the key roughly twice per
second, which is ample for most purposes.
The distance that the key can be transmitted is a more important
technical limitation. Most experts believe Geneva’s group demonstration of
67 km transmission through telecommunication cable is near the limit, although
transmission along optical fibre could be some 100 km. Another possibility
considered is transmission through space, and eventually via satellite.
Physicists have been able to transmit quantum keys for cryptography over
distances of 23.4 kilometres in free space, but all these involved only single
photons, not entangled pairs of photons.
In June 2003, a new distance record was broken. Markus Aspelmeyer and
colleagues at the University of Vienna, Austria, showed it is possible for two
photons to travel a total of 600 metres through free space and still remain
entangled. The previous record for entanglement in free space was a few
metres.
The Vienna group used a crystal with nonlinear optical properties to
split photons with a wavelength of 405 nanometres into pairs of entangled
photons with wavelengths of 810 nanometres. These photons then passed through
optical fibres to telescopes that focussed them onto a second pair of
telescopes. One receiving telescope was 500 metres away on the opposite side of
the river Danube, while the other was about 150 metres away. By comparing the
photons detected by the two receiving telescopes, the team confirmed that the
photons had remained entangled over a distance of 600 metres in free space.
There was no direct line of sight between the receiving microscopes.
Quantum teleportation
Quantum teleportation was discovered by Charles Bennett in 1993.
Teleporting ordinarily means sending matter instantaneously through empty
space, rather in the manner of Captain Kirk’s request: "Beam me up,
Scotty", in the StarTrek television series. But quantum teleporting is less
dramatic, it describes the transport of a quantum state from one place to
another, without actually transporting material. It is an alternative way of
transmitting quantum information.
Imagine Alice and Bob already in possession of a pair of entangled
qubits or photons. If Alice prepares another photon (to be teleported) in a
certain quantum state, she can pass this quantum state onto Bob by performing a
measurement of a joint property of the two photons in her possession
that will transform Bob’s qubit into one of four states, depending on the
four possible (random outcomes) of Alice’s measurement. Alice’s
measurement entangles the two photons in her possession, and disentangles
Bob’s photon, thereby steering it into a certain state. Alice then
communicates the outcome of her operation to Bob. In this way, Bob knows how to
transform his photon into the quantum state of Alice’s photon. Alice and
Bob have effectively used their shared entangled state as a quantum
communication channel to destroy the state of a photon in Alice’s part of
the universe and recreate it in Bob’s part of the universe.
Who wants quantum cryptography?
Physicists want it as an intellectual challenge, that much is obvious.
But who will benefit? Organisations obsessed with secrecy will be the first to
want to use quantum cryptography for transferring information within a single
city, such as government offices, banks and businesses. In the longer-term, the
military and big governments will probably be the most dedicated customers.
Don’t forget, terrorist groups, too, could use quantum cryptography
to plan their activities and escape ‘intelligence’.
Or maybe no one can prevent clever snoopers using weak measurement to
spy and get all the secrets. This is perhaps the best argument for total
transparency in the coming quantum world.
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