Quantum Computation and Cryptography
We are a small sub-group of the mathematical physics group in the Mathematical Institute, studying a range of topics in Quantum Information, particularly Quantum Computation and Quantum Cryptography. We have particularly strong ties to the Centre for Quantum Technologies at the National University of Singapore, and the numerous quantum information/computation/technologies groups in Oxford, whose aggregated information may be found here.
We are always interested to receive applications from strong candidates for PhD positions. These applications are handled centrally. For more information, please see the main university pages.
Professor of Quantum Physics and Lee Kong Chian Centennial Professor
Lecturer in Mathematics at Royal Holloway University of London
Our interests range broadly across Quantum Information. We describe a couple of topics which are currently our main focus.
According to Quantum Mechanics, given the most precise description possible of how things are now, the most you can do is predict the probability that things will turn out one way or another. Many people (including, famously, Albert Einstein) found this a disturbing feature of the theory, which suggested to them that Quantum Mechanics was not the real theory of nature, and that we were missing something. However, in a pivotal paper in 1964, John Bell showed a way of processing measurement results from certain experiments so that there is a threshold value, a maximum value which can be obtained by models (known as Local Hidden Variable models) which describe all possible models of physics which obey two fundamental properties: the theories should not be capable of transmitting information faster than the speed of light, and measurement results should be predetermined. However, the way that Bell combined these measurement results also predicted that a Quantum Mechanical system would exceed this threshold value, i.e., one of those assumptions on the nature of the physical world must be false. This prediction has been confirmed by numerous experiments in the intervening years.
To most, this unpredicatability of measurement results would present a problem. However, cryptographers look to benefit from such features. Information is always represented by measurable physical properties, and if such properties exist then, their value can be predicted with certainty without in any way disturbing a system. This is just a description of a perfect eavesdropping. Conversely, if such properties do not exist prior to measurements, then there is nothing to eavesdrop on. Hence, measuring the so-called Bell Inequalities in an experiment provides a test of just how much a quantum transmission has been eavesdropped. Remarkably, this requires very little by way of assumptions about the protocols that are being followed - it doesn't matter what devices we are using, or if we even trust the person who manufactured the devices or not - provided a Bell inequality is violated, we can use the measurement results to communicate securely. This is known as Device Independent cryptography. These ideas were first applied to the classic task in cryptography; key distribution, although has since been applied in various other instances such as the expansion of a sequence of random numbers.
Quantum cryptography is a rapidly maturing technology; one can even buy commercial systems based on the fundamental principles of communication secured by the laws of quantum physics, rather than relying on unproven assumptions about the difficulty of inverting certain mathematical functions (which is the basis of most cryptography currently in use). However, one major limiting factor is signal degredation with distance; experimentally, it is very hard to set up key distribution between two parties who are deparated by a distance of more than about 100km. Theoretically, we know how to overcome these problems by using quantum repeaters. However, an essential component of this technology is the ability to store a quantum state for a long time, which remains a practical challenge. We are studying some of the theoretical concepts associated with the storage of quantum information in the presence of errors with the aim of understanding different techniques for tolerating these errors, and consequently reducing experimental requirements.
Architectures for Quantum Computation
Equally compelling, but experimentally more challenging, would be the realisation of a fully-fledged quantum computer. Once we can build one of these devices, it will be possible to solve some computational tasks massively faster than the best known algorithms that run on today's computers. Theoretically, a sufficient set of conditions for implementing a quantum computer is known - one has to be able to perform rotations on every individual element of the computer (known as a qubit) and interact any arbitrary pair of qubits. However, to date, all designs for a quantum computer struggle to realise at least one aspect of this. We are therefore interested in how one might tailor the theoretical requirements for a quantum computer to de-emphasise the particularly problematic components.
For instance, we recently showed that if a quantum system is described by a particular class of intrinsic dynamics, those dynamics themselves can be used to implement the majority of the computational tasks, one one only has to directly manipulate the state of a single qubit.