Quantum information science: tools and applications for fundamental physics (Ext.)

点击翻译按钮获取中文摘要

This is an extension of the Fellowship 'Quantum information science: tools and applications for fundamental physics'. The fellowship initially focused on applying tools from computer science to study thermodynamics and statistical mechanics, and the extension will focus on applying them to better understand quantum gravity.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 develop and apply tools from computer science and quantum information theory to other areas of physics, in a way which aims to deepen our understanding of fundamental laws. Our current theory of gravity -- Einstein's general relativity -- is the theory of space-time and it is incompatible with quantum mechanics. Finding a consistent theory of gravity and quantum mechanics is one of the holy grails of modern physics. One of the few clues we have to reconciling the two theories is the black hole. These are objects which are so heavy, not even light can escape from them. Tantalizing hints from their study, such as the discovery that their entropy is proportional to their area, and that this area obeys thermodynamical laws suggest that information plays a fundamental role in quantum gravity. We know from previous work that thermodynamics is a field which can also be understood, in terms of information theory. Likewise, the black hole information problem, posed by Hawking, appears to suggest that black holes destroy information. If they do, then this requires radical changes to fundamental physics, and if instead they do preserve information, then we need to understand how this can be the case. The black hole information problem is precisely about the way information behaves and is stored in space-time. All these clues strongly suggests that in order to understand quantum gravity, we need to use tools from quantum information theory. It is thus no surprise, that increasingly, quantum gravity researchers are turning to quantum information theory to provide clues as to what a consistent theory of gravity will look like. This has led to a flurry of new ideas in the field. For example, there are some indications that entanglement (an important property of some quantum states) plays an important role in determining the geometry of space time. Likewise there are some indications that nature is holographic, in that information about a region can be described on its boundary (indeed this is the case for black holes). Understanding holography, and whether it holds, is another example where information theory is important, since holography is a statement about how and where information is stored. This project aims to apply and strengthen existing tools from quantum information theory -- many of them developed by the PI -- so that we may better understand what a consistent theory of quantum field theory and space-time will look like.