Quantum information science: tools and applications for fundamental physics

计算机科学为物理学带来了一种新的范式，人们可以从信息操纵的角度来理解自然法则。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，这使得我们对量子力学的理解有了根本性的突破，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。拟议中的研究将把计算机科学的工具应用到物理学的其他领域，目的是加深我们对基本定律的理解。我们将使用的来自信息理论的数学工具是非常通用的，因为任何理论都可以被认为是信息的进化和操纵，因此它们可以应用于物理学的许多不同领域。这些工具可以应用的一个例子是热力学领域。热力学定律支配着我们周围的世界——它告诉我们，在寒冷的房间里，一杯热茶会变冷，而不是变热；他们告诉我们，除非我们保持警惕，否则我们的房子将变得不整洁，而不是自然整洁；但热力学定律只适用于大物体，当涉及许多粒子时。热力学定律能否适用于小型系统，比如目前在实验室制造的微型马达？或者甚至是量子系统？信息理论的工具可以用来做到这一点，这项研究的目的是为量子系统构建热力学定律。更重要的是，大自然似乎对微观设备和热机施加了根本性的限制。量子热机有时会出现故障。我们无法从量子系统中获得最佳的能量。这意味着，如果应用于小系统，目前的热力学定律从根本上是不正确的，许多标准定律需要修改。另一个例子是，我们目前的热力学定律告诉我们，热力学过程可以是可逆的：一台冰箱只是一个反向的热泵。但在纳米尺度上，可逆性被打破了。这项研究的结果在小型系统中有广泛的应用，从纳米级设备到生物马达，到量子计算机等量子技术，再到纳米机器人喝分子量的茶。这些相同的数学工具非常通用，可以应用于其他情况，例如，更好地理解黑洞。这也许并不令人惊讶，因为黑洞的关键特性之一是它们的行为就像具有温度和熵的热力学物体。事实上，霍金提出的黑洞信息问题正是关于信息的行为方式。我们还可以应用信息理论的技术来更好地理解量子理论的基本特征，我们可以问一些问题，比如为什么量子理论必须是这样的。例如，最近，我们使用计算机科学的工具来检查海森堡的不确定性原理（它说你永远不可能同时知道粒子的位置和动量）和量子非局部性（当你测量纠缠粒子时发生的强相关性）之间的联系。这两个基本特征被认为是分开的和不同的概念。但是使用计算机科学的工具，人们会发现它们是密不可分的。正是测不准原理决定了量子非定域性的强度。

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.