Quantum Foundations and Quantum Information

量子基础和量子信息

• 批准号: 0456951
• 负责人: Robert Griffiths
• 金额: --
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-08-01 至 2008-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0456951&HistoricalAwards=false
• 关键词: Quantum; Foundations; Information

Quantum Foundations and Quantum Information Project Summary 1. Intellectual merit Advances in the study of quantum foundations using the (consistent or decoherent) histories approach have made it possible to resolve, or at least better understand, a number of the paradoxes which have perplexed students of quantum mechanics ever since it was developed in the early twentieth century. The fruits of this work, in particular the possibility of applying probability theory to microscopic quantum systems in a consistent way, will be used to study some of the remaining conceptual difficulties of quantum theory, in particular the nature of quantum locality: are there or are there not in the quantum world nonlocal influences producing action at a distance contrary to relativity theory? In addition, consistent probabilistic ideas will be employed to elucidate the physical significance of some of the standard tools used by quantum physicists, such as density operators and POVMs, whose mathematical de nitions are clear and simple, but whose intuitive significance is often very obscure and the subject of dispute. Various problems in quantum optics, including the nature of the quantum jumps exhibited by an ion in a trap when illuminated in a suitable way by laser light, will be studied using simplified quantum models whose properties are easily calculated and thus make it possible to get to the essential ideas behind quantum processes without lengthy mathematical calculation. Finally, the nature of the "weak measurements" introduced by Aharonov and collaborators will be studied using POVMs and statistical correlations. The nature of quantum information, as it arises in quantum computation and quantum cryptography, will be investigated by applying ideas from standard (classical) information theory, as developed by Shannon and his successors, to the statistical correlations between microscopic quantum systems corresponding to consistent sets of probabilities generated by different types of entangled state. A special focus will be on the question of how much information of a particular type about one quantum system is present in a different system due to their statistical correlation. This will be studied both for quantum communication channels, where one is interested in correlated quantum properties at two different times, and for entangled states, where the properties are those of two different systems at the same time. The question of how entangled quantum states can be distinguished, and the nature of the statistical correlations that arise during the process of decoherence, are among the subjects to be investigated from this point of view. 2. Broader impacts 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 studying physics and computer science. Postdoctoral research associates will have an opportunity to sharpen their skills while participating in this research group, making them more valuable members of the scientific community. Students and postdocs will take part in an ongoing seminar series in quantum information, and occasional courses which address these subjects, both of which attract other scientists and science students living in Pittsburgh. The results of foundations research as embodied in occasional lectures and articles written for teachers, possibly even a textbook, will help improve the teaching of quantum mechanics, a subject which students always find very difficult, not least because of the conceptual confusion produced by unresolved foundations issues of the type this research is designed to clear up.

量子基础和量子信息项目摘要1。知识价值使用（一致或退相干）历史方法研究量子基础的进展使得解决或至少更好地理解自世纪初量子力学发展以来一直困扰着量子力学学生的一些悖论成为可能。这项工作的成果，特别是概率论以一致的方式应用于微观量子系统的可能性，将被用来研究量子理论的一些剩余的概念性困难，特别是量子定域性的性质：在量子世界中，是否存在或不存在非定域影响，产生与相对论相反的距离作用？此外，一致的概率思想将被用来阐明量子物理学家使用的一些标准工具的物理意义，如密度算符和POVM，它们的数学定义是清晰和简单的，但其直观的意义往往是非常模糊的和有争议的主题。量子光学中的各种问题，包括当激光以适当的方式照射时阱中离子所表现出的量子跳跃的性质，将使用简化的量子模型进行研究，这些模型的性质很容易计算，因此可以在没有冗长的数学计算的情况下获得量子过程背后的基本思想。最后，Aharonov及其合作者引入的“弱测量”的性质将使用POVM和统计相关性进行研究。量子信息的本质，因为它出现在量子计算和量子密码学，将通过应用标准（经典）信息理论的思想，由香农和他的继任者开发，微观量子系统之间的统计相关性对应于不同类型的纠缠态产生的一致的概率集进行研究。一个特别的焦点将是关于一个量子系统的特定类型的信息由于它们的统计相关性而存在于不同系统中的问题。这将研究量子通信信道，其中一个感兴趣的是在两个不同的时间相关的量子特性，和纠缠态，其中的属性是两个不同的系统在同一时间。如何区分纠缠量子态的问题，以及退相干过程中出现的统计相关性的性质，都是从这个角度研究的主题。2.研究工作将通过为学习物理和计算机科学的学生提供研究项目，为麦基-梅隆大学本科和研究生阶段的教育计划做出贡献。博士后研究人员将有机会在参加这个研究小组的同时提高他们的技能，使他们成为科学界更有价值的成员。学生和博士后将参加正在进行的量子信息系列研讨会，以及涉及这些主题的偶尔课程，这两个课程都吸引了居住在匹兹堡的其他科学家和理科学生。基础研究的结果体现在偶尔的讲座和为教师写的文章中，甚至可能是教科书，将有助于改善量子力学的教学，这是一个学生总是觉得非常困难的主题，尤其是因为未解决的基础问题所产生的概念混乱，这种研究旨在澄清。