Quantum Foundations and Quantum Information

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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.