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

这是“量子信息科学：基础物理的工具和应用”奖学金的延伸。该奖学金最初专注于应用计算机科学的工具来研究热力学和统计力学，扩展的重点将是应用它们来更好地理解量子引力。计算机科学已经导致了物理学的一个新范式，即人们从信息操纵的角度来理解自然规律。计算机科学也有工具可以用来分析这些操作的效率。在过去的二十年里，这使我们对量子力学的理解取得了根本性的突破，我们现在知道，量子计算机可以比经典计算机快得多，量子粒子可以用来私下传输信息，这在经典世界是不可能的。这项拟议的研究将开发和应用计算机科学和量子信息论的工具到物理学的其他领域，旨在加深我们对基本规律的理解。我们目前的引力理论--爱因斯坦的广义相对论--是时空理论，它与量子力学不相容。找到引力和量子力学的一致理论是现代物理学的圣杯之一。我们能够调和这两种理论的为数不多的线索之一就是黑洞。这些物体太重了，甚至连光都无法逃脱。他们的研究提供了一些诱人的线索，比如发现它们的熵与它们的面积成正比，以及这个区域遵守热力学定律，这表明信息在量子引力中扮演着基本的角色。我们从以前的工作中知道，热力学是一个也可以从信息论的角度来理解的领域。同样，霍金提出的黑洞信息问题似乎表明黑洞破坏信息。如果他们这样做了，那么这就需要对基础物理进行根本性的改变，如果他们确实保存了信息，那么我们需要理解这种情况是如何发生的。黑洞信息问题恰恰是关于信息在时空中的行为和存储方式。所有这些线索都强烈表明，为了理解量子引力，我们需要使用量子信息论中的工具。因此，量子引力研究人员越来越多地转向量子信息理论，以提供一致的引力理论是什么样子的线索，这就不足为奇了。这导致了该领域的一系列新想法。例如，有一些迹象表明，纠缠(某些量子态的一个重要性质)在决定时空几何方面发挥着重要作用。同样，有一些迹象表明，自然界是全息的，因为关于一个区域的信息可以在其边界上描述(事实上，黑洞就是这种情况)。理解全息术，以及它是否成立，是信息论很重要的另一个例子，因为全息术是关于信息如何存储以及存储在哪里的声明。这个项目旨在应用和加强量子信息理论的现有工具--其中许多工具是由PI开发的--以便我们可以更好地理解量子场论和时空的一致理论将是什么样子。

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.