Quantum Foundations and Quantum Information

我们将使用一致的量子力学公式来研究量子信息中的各种问题，目的是从非常基本的角度理解量子信息如何扩展或修改香农及其继任者发展的关于普通或经典信息的众所周知的想法。特别是，经典信息处理不同各方之间的统计相关性，如信息源和接收者，而量子信息预计具有类似的结构。然而，必须谨慎对待量子力学中的统计关联，以免陷入量子基础研究中众所周知的悖论。在这项工作中，通过密切关注不同类型的量子信息，并找出一种类型的信息在一个位置的存在与在其他位置的相同或不同类型的信息的存在或不存在之间的关系，这些悖论将被避免。由三部分组成的量子系统将是研究的重点，因为人们对它们的信息理论性质仍然只有部分了解。此外，还将寻找在两个不同位置高效地对关联(纠缠)量子系统进行操作的方法，这需要遵守量子力学定律的通信和其他资源。这一领域的研究应该会让人们更好地理解量子密码学方案中信息是如何从一个地方移动到另一个地方的，以及当信息可能去到错误的地方(去相干)时如何纠正量子计算机中的错误。此外，还将致力于澄清量子信息研究中使用的一些基本量子概念，以便使它们更直观，而不仅仅是形式上的数学表达式。其中包括用于计算量子系统概率的系综及其相关的密度运算符，以及被称为POVM的某些类型的测量。对量子信息的更好理解将在两个不同的层面上影响物理教学。第一个与量子信息和量子计算的教学课程有关。来自不同学科的学生，包括数学、计算机科学、电气工程以及物理，都对这门学科感兴趣，如果能更清楚地介绍它的基本原理，将会受益。其次，由于量子信息如今是许多量子物理入门课程的组成部分，对量子力学的更好理解应该会让所有想要认真学习它的人更容易接触到它。这项研究工作将通过为包括攻读博士学位的学生在内的学生提供研究项目，为卡内基-梅隆大学的本科生和研究生教育项目做出贡献。博士后研究助理将有机会在参与研究的同时磨练自己的技能，使他们成为科学界更有价值的成员。学生和博士后助理将参加有关这些主题的研讨会和课程，这两个主题都吸引了居住在匹兹堡的其他科学家和理科学生。在匹兹堡开始的量子力学和量子信息教学的改进最终将证明对其他地方的大学生有利，物理学家对量子力学的更好理解应该有助于更广泛的公众对这一主题的更好理解。

Various issues in quantum information will be studied using a consistent formulation of quantum mechanics with the aim of understanding, from a very fundamental perspective, how quantum information extends or modifies the well-known ideas of ordinary or classical information developed by Shannon and his successors. In particular, classical information deals with statistical correlations between different parties, such as an information source and a receiver, and quantum information is expected to have a similar structure. However, statistical correlations in quantum mechanics have to be treated with care so as not to run into paradoxes which are well known from the study of quantum foundations. In this work these paradoxes will be avoided by paying close attention to different types of quantum information, and working out how the presence of one type of information at one location is related to the presence or absence of the same or a different type of information at some other location. Quantum systems with three parts will be the focus of study, as their information-theoretical properties are still only partially understood. In addition, there will be a search for ways of efficiently carrying out operations on correlated (entangled) quantum systems at two different locations, requiring communication and other resources which respect the laws of quantum mechanics. Research in this area should lead to a better understanding of how information moves around from one place to another in schemes for quantum cryptography, and how to correct errors in a quantum computer when information may be going to the wrong place (decoherence). In addition, some effort will be devoted to clarifying some of the fundamental quantum concepts that are employed in quantum information studies in order to make them more intuitive, not simply formal mathematical expressions. These include ensembles and their associated density operators used in calculating probabilities in quantum systems, and certain types of measurements known as POVMs. A better understanding of quantum information will affect physics teaching at two different levels. The first has to do with teaching courses in quantum information and quantum computation. Students from a variety of disciplines, including mathematics, computer science, and electrical engineering, as well as physics, are interested in the subject, and would benefit from a clearer presentation of its fundamental principles. Second, since quantum information is nowadays a component of many introductory quantum physics courses, an improved understanding should make quantum mechanics more accessible to all who want to study it in a serious way. The research effort will contribute to the education program at Carnegie-Mellon University at both the undergraduate and graduate levels, through providing research projects for students, including those working towards a PhD. Postdoctoral research associates will have an opportunity to sharpen their skills while participating in the research, making them more valuable members of the scientific community. Students and postdoctoral associates will take part in seminars and courses which address these subjects, both of which attract other scientists and science students living in Pittsburgh. Improvements in teaching quantum mechanics and quantum information initiated in Pittsburgh will eventually prove beneficial to university students elsewhere, and a better understanding of quantum mechanics on the part of physicists should contribute to a better appreciation of this topic by the broader public.