Recent research into quantum information theory has led to a deeper understanding of quantum theory, and the development of powerful new techniques and concepts which can be applied to other areas of fundamental physics. Three areas I am particularly interested in are:

1) Foundations of statistical mechanics Everyone knows that if you leave a cup of hot coffee on your desk, it will eventually cool down to room temperature, but deriving this result from the microscopic laws is surprisingly difficult - in fact we still don't have a complete solution. Recently, we have been able to prove that almost any quantum system interacting with a large environment will equilibrate, moving towards a static state and staying there for almost all times. This provides a firmer foundation for statistical mechanics and thermodynamics, and suggests that equilibration happens even at the microscopic scale, where we normally imagine a flurry of moving particles.

2) Exploring quantum theory in a general framework To gain a better understanding of quantum theory, it is helpful to compare and contrast it with a broad range of alternative theories. These investigations can be conducted in a general framework containing almost any conceivable theory, some of which are even stranger than quantum theory. Many properties of quantum theory are generic in this framework, whilst other properties seem more special, such as the ability to reversibly transform between any two states. Is quantum theory the most general reversible theory? Investigating such questions may lead to a better understanding of why nature is quantum, or help us go beyond it to a deeper theory.

3) Particle physics in discrete space and time How would fundamental particles behave if space and time were really discrete (like a giant chess board and a digital clock), rather than being smooth and continuous? One can use ideas from quantum information theory to address this question, and give a natural interpretation of the speed of light, as moving one 'square' in one tick of the clock. If the size of the squares in the discrete model is sufficiently small, particles can appear to move smoothly in any direction. Could the world really be like this? If so, studying such models may revolutionise our understanding of nature. However, even if it is not fundamentally true, this approach may lead to new simulation methods.