Quantum Foundations and Information Theory Using Consistent Histories

20世纪二三十年代量子力学的发展留下了许多未解决的矛盾。虽然这些并没有阻止量子理论在物理和化学中大量不同问题的应用，但它们使学生很难学习这门学科，并且可能表明在目前所理解的量子力学中存在一些逻辑上的不一致性。这些悖论，以及它们通常被认为暗示的相关的非局部影响，将使用来自量子理论的一致历史公式的一些相对较新的想法来研究，量子理论是标准量子力学的扩展，它允许它以一致的方式应用于涉及三个或更多连续时间的事件序列。这项研究将关注这些所谓的非局部影响是真实的，还是由于未能以与量子理论基础数学一致的方式应用量子思想而导致的。标准量子理论利用密度矩阵提供量子系统的统计描述。然而，密度矩阵的物理解释并不十分清楚。这将通过把密度矩阵仅仅作为量子统计力学更一般的表述的一个方面来研究，这种表述是通过使用一致的历史方法实现的。在这种情况下，将考虑量子光学和原子物理学中使用的标准密度矩阵理论的某些扩展。这一领域的进展将对量子基础和量子信息理论都有价值。量子信息论关注的是开发用于传输量子态、量子密码学和量子计算等目的的量子效应所需的概念和数学工具。在量子信息理论的许多主题中发挥核心作用的数学方法将通过观察简单的例子来研究，并寻找可以在更一般的情况下证明成立的性质。此外，将利用基于一致历史的思想来解决提高量子通信和量子计算机效率的问题。

A number of unresolved paradoxes were left over from the development of quantum mechanics in the 1920's and 1930's. While these have not prevented the application of quantum theory to a large number of different problems in physics and chemistry, they make it hard for students to learn the subject, and might suggest that there is some logical incoherence in quantum mechanics as currently understood. These paradoxes, and the associated nonlocal influences which they are often thought to imply, will be studied using some relatively new ideas coming out of the consistent histories formulation of quantum theory, an extension of standard quantum mechanics which allows it to be applied in a consistent way to sequences of events involving three or more successive times. The study will focus on whether these purported nonlocal influences are real, or result from failing to apply quantum ideas in a way which is consistent with the basic mathematics which underlies quantum theory. Standard quantum theory makes use of density matrices to provide a statistical description of a quantum system. However, the physical interpretation of density matrices is not very clear. This will be studied by regarding density matrices as just one aspect of a more general formulation of quantum statistical mechanics made possible by the use of consistent history methods. In this context, certain extensions to standard density matrix theory that are used in quantum optics and atomic physics will be taken into account. Advances in this area will be of value for both quantum foundations and quantum information theory. Quantum information theory is concerned with developing the conceptual and mathematical tools needed when using quantum effects for purposes of transmitting quantum states, quantum cryptography, and quantum computation. Mathematical methods which play a central role in many topics in quantum information theory will be studied by looking at simple examples, and looking for properties which can be shown to hold in more general situations. In addition, the problem of improving efficiency in quantum communication and quantum computers will be addressed using ideas based upon consistent histories.