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.
