Multiplying two large, or even very large numbers is easy and
does not take long on a computer. The reverse operation, i.e. finding the factors of a large number, is hard. If the number is very large, and the factors are not simple, the factorisation can take an extremely long time. This is the basis for one of the most common methods of transmitting confidential information, for example bank transactions on the internet.
The old-fashioned way
For information that needs to be secure for a long time, there is a cloud on the horizon, however. It was discovered by Peter Shor in 1994 that a computer based on the principles of quantum mechanics would in principle be able to factorise large numbers much more quickly than ordinary computers. Such quantum computers are still a distant prospect, however, because their operation depends on the detailed control of the quantum states of large numbers of atoms. So far, one has only been able to achieve such control for small numbers of atoms or other elementary quantum systems, i.e. the polarisation state of light. Nevertheless, considerable progress is being made and it is not unthinkable that in 20 years or so, the first prototypes of quantum computers will be constructed. Military secrets, for example, may need to be secure for much longer.
The modern form of exchanging information
Fortunately, quantum mechanics also provides a way of improving the security of information transmission! This was proposed by Charles Bennett in 1988. His method is quite simple and relies on entangled pairs of qubits � the quantum analogue of bits. Entanglement was shown by Schroedinger to be a crucial feature of quantum mechanics. One can produce pairs of photons, the particles of light, in a state where neither has a determined polarisation, but if one measures the polarisation of one, a subsequent measurement of that of the other always results in the same value. This is a kind of action at a distance since the two photons can be arbitrarily far apart! Einstein objected to quantum mechanics on these grounds, but the effect has now been conclusively demonstrated experimentally. Bennett's proposal is for Alice to send one half of such an entangled pair to Bob and to measure the polarisation of the other half herself. By doing this repeatedly, they can communicate a secret code. If there is an eavesdropper, measuring the state of the photons on the way to Bob, this will destroy the coherence between Alice and Bob's photons, and this can easily be detected by selecting a subset and comparing these publicly over the phone. This scheme has in fact already been realised in experiments over considerable distances and is therefore much further advanced than the development of quantum computers.
Future information transmission?
In both applications of quantum mechanics, the information being processed can easily be corrupted by errors since quantum states of microscopic systems are extremely fragile. In practice, one will need to introduce error-correcting codes. For classical information (bits) this is easy. For example, one can send each bit three times. Then, if one of the bits is corrupted during transmission, it can be restored. Usually, the chances of two of the bits being corrupted at the same time are extremely small. (Not always. Data from astronomical satellites are encoded much more elaborately, for example.) For qubits, i.e. quantum information, there is a problem: it is not possible to duplicate an arbitrary unknown state! This is called the no-cloning theorem. In an important breakthrough, Shor and Andrew Steane showed in 1995, that despite this problem, it is still possible to devise quantum error-correcting codes. Their code was not optimal and improved versions have since been proposed. Effective error-correcting codes are obviously very important and much research is still being done in this area. The School of Theoretical Physics is involved in research in the area of quantum information theory.
Contact: Professor Tony Dorlas, Director,
School of Theoretical Physics,
Dublin Institute for Advanced Studies,
10 Burlington Road, Dublin 4;
Tel: (01) 6140146;
E-mail:
[email protected]
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