Operator Structures and Methods in Quantum Error Correction, Quantum Privacy, and Entanglement Theory

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We are on the doorstep of a “quantum revolution” in many areas of modern science, perhaps most significantly in the development of new types of technologies based on quantum information science. Quantum information is the umbrella term that has evolved to encompass such disciplines as quantum computing, quantum cryptography, quantum information theory, and quantum information processing. Canada has positioned itself as a world leader in these theoretical and experimental efforts, and the Canadian mathematical community in particular has identified quantum information as a key research area in its recent long range plan. The primary goal of the proposed research is to investigate central foundational problems in quantum information, with an approach rooted in mathematics. Specifically, the proposed research program of David Kribs goes directly to the heart of the mathematical foundations of the subject; intensifying and broadening his investigations in the fundamental areas of quantum error correction, quantum privacy, and quantum entanglement theory, with a methodological approach based on core operator theoretic mathematical structures and techniques. As part of the proposed research, Kribs will also continue his efforts in the training of highly qualified personnel in these emerging and maturing disciplines and the underlying mathematics, and at generating interactions between the different scientific communities that intersect with the heavily interdisciplinary areas of quantum information.