*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*

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.

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 2^{N} states each with its own quantum amplitude.

׀ψ› = g_{0}?0_{1}0_{2}0_{3…..}0_{N}› + g_{1}?0_{1}0_{2}0_{3…..}1_{N}› + g_{N-1}?1_{1}1_{2}1_{3…..}1_{N}› (2)

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 <wwwi-sis.org.uk>)?

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:

׀ψ› = ?0_{A}0_{B}› + ׀1_{A}1_{B}› (1)

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 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.

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.

*Article first published 22/03/04*

- Monroe C. Quantum information processing with atoms and photons.
*Nature*2002, 416, 238-46. - Bennett C. and Brassard G. Quantum cryptography: public key distribution and coin tossing.
*Proc IEEE Int. Conf. Comp. Syst. Signal Proc*. 1984, 11, 175-9. - "Can you keep a secret?" by Erica Klarreich,
*Nature*2002, 418, 270-2. - "Entanglement bridges the Danube",
*Physicsweb*June 30, 2003. - Bennett CH
*et al*. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky Rosen-channels.*Phys Rev Lett*1993, 1895-99. - Ho MW.
*The Rainbow and the Worm, The Physics of Organisms*, World Scientific, Singapore, 1993, 2^{nd}ed. 1998, reprinted 1999, 2001, 2003.

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