Quantum Foundations and Quantum Information

量子基础和量子信息项目综述1.使用(一致或退相干)历史方法研究量子基础的智力进步使人们有可能解决，或者至少更好地理解自二十世纪初量子力学发展以来困扰着量子力学学生的一些悖论。这项工作的成果，特别是将概率论以一致的方式应用于微观量子系统的可能性，将被用于研究量子理论的一些剩余概念困难，特别是量子局域性的性质：在量子世界中，是否存在非局域影响，在与相对论相反的距离产生作用？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，它们的数学定义清晰而简单，但其直观意义往往非常模糊和有争议的主题。量子光学中的各种问题，包括陷阱中的离子在激光以适当的方式照射时所表现出的量子跃迁的性质，将使用简化的量子模型来研究，这些模型的性质很容易计算，从而使人们能够在不进行冗长的数学计算的情况下获得量子过程背后的基本概念。最后，Aharonov和合作者引入的“弱测量”的性质将使用POVM和统计关联进行研究。在量子计算和量子密码学中出现的量子信息的本质，将通过应用香农和他的继任者发展的标准(经典)信息论的思想来研究微观量子系统之间的统计关联，这些统计关联对应于由不同类型的纠缠态产生的一致概率集。特别关注的问题是，由于统计相关性，关于一个量子系统的特定类型的信息在不同的系统中存在多少。这将在量子通信信道和纠缠态两个方面进行研究，在量子通信信道中，人们对两个不同时间的关联量子属性感兴趣，而在纠缠态中，属性是两个不同系统的属性。如何区分纠缠量子态的问题，以及在退相干过程中出现的统计关联的性质，都是从这个角度进行研究的主题。2.更广泛的影响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，为卡内基-梅隆大学的本科生和研究生教育计划做出贡献。博士后研究助理将有机会在参加这个研究小组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。学生和博士后将参加正在进行的量子信息系列研讨会，以及针对这些主题的不定期课程，这两者都吸引了其他居住在匹兹堡的科学家和理科学生。基础研究的成果体现在偶尔为教师撰写的讲座和文章中，甚至可能是一本教科书，这将有助于改善量子力学的教学，学生们总是发现这门学科非常困难，尤其是因为这项研究旨在解决的这类悬而未决的基础问题造成了概念上的混乱。

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.