Computer science has led to a new paradigm in physics, where one understands the laws of nature in terms of the manipulation of information. Computer science also has tools which can be used to analyse how efficient these manipulations are. In the last two decades, this has led to fundamental breakthroughs in our understanding of quantum mechanics, and we now know that quantum computers can be much faster than classical computers, and that quantum particles can be used to transmit information privately, in a way that is impossible in the classical world. The proposed research will apply tools from computer science to other areas of physics, in a way which aims to deepen our understanding of fundamental laws. The mathematical tools from information theory which we will use are very general since any theory can be thought of as evolution and manipulation of information, and so they can be applied to many different areas of physics.
One example where these tools can be applied, is in the field of thermodynamics. The laws of thermodynamics govern much of the world around us - they tell us that a hot cup of tea in a cold room will cool down rather than heat up; they tell us that unless we are vigilant, our houses will become untidy rather than spontaneously tidy;. But the laws of thermodynamics only apply to large objects, when many particles are involved. Can the laws of thermodynamics be applied to small systems, such as the kind of microscopic motors currently been fabricated in labs? Or perhaps even quantum systems? Tools from information theory can be used to do so, and this research aims to construct laws of thermodynamics for quantum systems. What's more, it appears that nature imposes fundamental limitations on microscopic devices and heat engines. A quantum heat engines will sometimes fail. We cannot extract energy optimally from a quantum system. This means that the present laws of thermodynamics are fundamentally incorrect if applied to small systems, and many of the standard laws need to be modified. Another example is that our current laws of thermodynamics tell us that thermodynamical processes can be made reversible: a fridge is just a heat pump in reverse. But at the nano-scale, reversibility breaks down. The results if this research have wide applications in small systems, from nano-scale devices, to biological motors, to quantum technologies such as quantum computers, and to nano-robots drinking molecular amounts of tea.
These same mathematical tools are very general and can be applied in other contexts, for example, to better understand black holes. This is perhaps not so surprising, since one of the key properties of black holes is that they behave like thermodynamical objects with a temperature and entropy. In fact, the black hole information problem, posed by Hawking, is precisely about the way information behaves. We can also apply techniques from information theory to better understand fundamental features of quantum theory, and we can ask questions such as why quantum theory has to be the way it is. For example, recently, we've used tools from computer science to examine links between Heisenberg's uncertainty principle (which says that you can never know a particle's position and momentum at the same time), and quantum non-locality (the strong correlations which occur when you measure entangled particles). These two fundamental features had been considered separate and distinct concepts. But using tools from computer science, one sees that they are inextricably linked. It is the uncertainty principle which determines exactly the strength of quantum nonlocality.
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