Device independent quantum key distribution and the limitations and uniqueness of quantum information processing

Information science is the study of how well we can communicate messages, keep secrets, compute mathematical functions and so on. In classical information science, information is encoded digitally. For example, if a switch can be either up or down, then it can store a single classical bit of information. Any classical computer, from an abacus to a modern desktop PC, could be seen as nothing but a collection of such switches, along with the means to flip them up and down. Of course the PC is much faster! Quantum information science is different because information is encoded in a quantum system, such as a spinning charged particle in a magnetic field. Such a particle is a bit like a switch, because it can be spinning in one, or in the other direction with respect to the field. But the particle can also be in what is called a superposition of the two. This is hard to visualize and in terms of the classical switch there is no analogue. Further, the quantum particle can be entangled with other particles, exhibiting an apparently instantaneous connection even though they are widely separated in space.These strange features make a big difference. By manipulating quantum systems, we can do things that are impossible using classical, digital devices. A quantum computer, for example, can factorize a large number extremely rapidly, whereas this is strongly believed to be a difficult problem for classical computers. Present day encryption is often based on the difficulty of factorizing numbers, thus a quantum computer could easily crack the codes that are used to protect credit card details. But quantum information science also provides the solution: using a technique called quantum key distribution, we can send secret messages in such a way that security is guaranteed by the laws of quantum theory.The first part of the project involves the theoretical development of a new idea for quantum key distribution. The novel feature is that the proof of security does not need to assume anything about the operation of the quantum devices employed. So if a device is supposed to measure the horizontal polarization of a photon, say, a user does not need to trust that it really is doing that. Unlike all existing approaches, the new idea does not even need to assume the correctness of quantum theory. The crucial assumption is something different, which is the physical impossibility of sending transmissions faster than light. The advantage of this is that secret messages can be secure even when the users are not physicists but commercial users who have obtained their equipment from a potentially untrustworthy source. But at present there is only a proof of principle that the idea will work: perfect noise-free conditions are assumed and the rate at which messages can be sent is too slow to be useful in practice. A main goal of the project is to develop the theory to the point where the idea is a viable real-world possibility.The second part of the project is less about practical application but aims to improve our understanding of quantum theory. Given any well developed physical model, one can ask, what would information processing be like if the universe were described by that model? Could we build computers even better than quantum computers? This is a good way of learning about the limitations of quantum information processing, as well as the successes. How special is quantum theory, and why did Nature choose this theory and not another? I have already developed a mathematical framework that enables us to write down a wide range of different physical models and then to explore these questions. The goal is to determine which features of quantum theory are generic, in the sense that they would be present in almost any possible theory, and which are unique. In particular, I have suggested that quantum theory is the best theory for computation out of all possible theories. If true, this would be a very deep fact about Nature.