Device independent quantum key distribution and the limitations and uniqueness of quantum information processing

信息科学是研究我们如何更好地交流信息，保守秘密，计算数学函数等等。在经典信息科学中，信息是数字编码的。例如，如果开关可以向上或向下，则它可以存储单个经典位的信息。从算盘到现代的台式电脑，任何一台古典电脑都可以被看作是一组这样的开关，沿着上下翻转的装置。当然PC更快！量子信息科学是不同的，因为信息是在量子系统中编码的，例如磁场中旋转的带电粒子。这样的粒子有点像开关，因为它可以相对于场朝一个方向旋转，也可以朝另一个方向旋转。但是粒子也可以是这两者的叠加态。这是很难想象的，在经典的开关方面，没有类似的。此外，量子粒子可以与其他粒子纠缠在一起，即使它们在空间中相距甚远，也会表现出明显的瞬时联系。这些奇怪的特征造成了很大的不同。通过操纵量子系统，我们可以做一些使用经典数字设备不可能做到的事情。例如，量子计算机可以非常迅速地分解一个很大的数字，而这对于经典计算机来说是一个很难的问题。目前的加密通常是基于数字分解的困难，因此量子计算机可以很容易地破解用于保护信用卡详细信息的代码。但是量子信息科学也提供了解决方案：使用一种称为量子密钥分配的技术，我们可以以量子理论定律保证安全的方式发送秘密消息。该项目的第一部分涉及量子密钥分配新思想的理论发展。新的特点是，安全性的证明不需要假设任何关于所使用的量子设备的操作。因此，如果一个设备应该测量光子的水平偏振，那么用户不需要相信它真的在做这件事。与所有现有的方法不同，新的想法甚至不需要假设量子理论的正确性。关键的假设是不同的，这是物理上不可能发送传输速度超过光速。这样做的好处是，即使用户不是物理学家，而是从潜在的不可信来源获得设备的商业用户，秘密消息也可以是安全的。但目前只有一个原理证明这个想法是可行的：假设完美的无噪声条件，消息发送的速度太慢，在实践中没有用处。该项目的一个主要目标是将理论发展到一个可行的现实世界的可能性。该项目的第二部分与实际应用无关，而是旨在提高我们对量子理论的理解。给定任何一个发展完善的物理模型，人们可能会问，如果宇宙是用这个模型来描述的，信息处理会是什么样子？我们能造出比量子计算机更好的计算机吗？这是了解量子信息处理的局限性以及成功的好方法。量子理论有多特别？为什么大自然选择了这个理论而不是另一个？我已经开发了一个数学框架，使我们能够写下各种不同的物理模型，然后探索这些问题。我们的目标是确定量子理论的哪些特征是通用的，也就是说它们几乎存在于任何可能的理论中，哪些是独特的。我特别指出，量子理论是所有可能理论中最好的计算理论。如果是真的，这将是一个关于自然的非常深刻的事实。

Information science is the study of how well we can communicate messages, keep secrets, compute mathematical functions and so on. In classical information science, information is encoded digitally. For example, if a switch can be either up or down, then it can store a single classical bit of information. Any classical computer, from an abacus to a modern desktop PC, could be seen as nothing but a collection of such switches, along with the means to flip them up and down. Of course the PC is much faster! Quantum information science is different because information is encoded in a quantum system, such as a spinning charged particle in a magnetic field. Such a particle is a bit like a switch, because it can be spinning in one, or in the other direction with respect to the field. But the particle can also be in what is called a superposition of the two. This is hard to visualize and in terms of the classical switch there is no analogue. Further, the quantum particle can be entangled with other particles, exhibiting an apparently instantaneous connection even though they are widely separated in space.These strange features make a big difference. By manipulating quantum systems, we can do things that are impossible using classical, digital devices. A quantum computer, for example, can factorize a large number extremely rapidly, whereas this is strongly believed to be a difficult problem for classical computers. Present day encryption is often based on the difficulty of factorizing numbers, thus a quantum computer could easily crack the codes that are used to protect credit card details. But quantum information science also provides the solution: using a technique called quantum key distribution, we can send secret messages in such a way that security is guaranteed by the laws of quantum theory.The first part of the project involves the theoretical development of a new idea for quantum key distribution. The novel feature is that the proof of security does not need to assume anything about the operation of the quantum devices employed. So if a device is supposed to measure the horizontal polarization of a photon, say, a user does not need to trust that it really is doing that. Unlike all existing approaches, the new idea does not even need to assume the correctness of quantum theory. The crucial assumption is something different, which is the physical impossibility of sending transmissions faster than light. The advantage of this is that secret messages can be secure even when the users are not physicists but commercial users who have obtained their equipment from a potentially untrustworthy source. But at present there is only a proof of principle that the idea will work: perfect noise-free conditions are assumed and the rate at which messages can be sent is too slow to be useful in practice. A main goal of the project is to develop the theory to the point where the idea is a viable real-world possibility.The second part of the project is less about practical application but aims to improve our understanding of quantum theory. Given any well developed physical model, one can ask, what would information processing be like if the universe were described by that model? Could we build computers even better than quantum computers? This is a good way of learning about the limitations of quantum information processing, as well as the successes. How special is quantum theory, and why did Nature choose this theory and not another? I have already developed a mathematical framework that enables us to write down a wide range of different physical models and then to explore these questions. The goal is to determine which features of quantum theory are generic, in the sense that they would be present in almost any possible theory, and which are unique. In particular, I have suggested that quantum theory is the best theory for computation out of all possible theories. If true, this would be a very deep fact about Nature.