Quantum Foundations and Information Theory Using Consistent Histories

在20世纪20年代的S和30年代的S期间，量子力学的发展留下了一些悬而未决的悖论。虽然这些悖论并没有阻止量子理论应用于物理和化学中的大量不同问题，但它们使学生很难学习这门学科，并可能表明目前所理解的量子力学中存在一些逻辑上的不一致。这些悖论以及它们通常被认为暗示的相关的非局域影响，将使用来自量子理论的一致历史公式的一些相对新的想法来研究，量子理论是标准量子力学的扩展，允许以一致的方式将其应用于涉及三个或更多连续时间的事件序列。这项研究的重点将是这些所谓的非局域影响是真实存在的，还是由于未能以一种与支撑量子理论的基本数学一致的方式应用量子思想所致。标准量子理论利用密度矩阵来提供对量子系统的统计描述。然而，密度矩阵的物理解释并不是很清楚。这将通过将密度矩阵视为量子统计力学的更一般公式的一个方面来研究，该公式通过使用一致的历史方法而成为可能。在此背景下，将考虑在量子光学和原子物理中使用的对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。量子信息理论致力于开发在使用量子效应传输量子态、量子密码学和量子计算时所需的概念和数学工具。在量子信息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，并寻找在更一般情况下可以证明成立的性质。此外，提高量子通信和量子计算机效率的问题将使用基于一致历史的想法来解决。

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.