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Event(s) on December 2017


  • Friday, 8th December, 2017

    Title: Matrix Problems and Techniques in Quantum Information Science
    Speaker: Prof. Chi-Kwong Li, Department of Mathematics, The College of William & Mary (USA) and Institute for Quantum Computing, University of Waterloo, U.S.A.
    Time/Place: 10:30  -  16:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Three lectures will be presented on some matrix problems and techniques in quantum information science. No quantum mechanics background is required. Audience should have the basic linear algebra knowledge. One may see the recent reprints and preprints of Li and his collaborators on arXiv to get some ideas about the topics he plans to present. Lecture 1 -- Optimization Problems in Quantum Information Science In the mathematical framework, quantum states are represented as density matrices, i.e., positive semidefinite matrices with trace one, and quantum operations are represented as trace preserving completely positive linear maps. In quantum information science, one often has to estimate various measures between different quantum states and quantum processes. One also needs to design quantum operations with special properties. These give rise to many optimization problems involving matrices and linear transformations. In this lecture, selected results, techniques, and open problems in this line of study will be described. Lecture 2 -- Numerical Ranges and Quantum Information Science In quantum mechanics, measurement operators or observable are represented as Hermitian matrices, and measurement are done by taking the inner product of the measurement operators and the states (represented as density matrices). The collection of such measurement values on states can be viewed as elements in the joint numerical range of the measurement operators. Also, in the study of quantum operations with special properties, and the quantum error correction codes of quantum channels, one can formulate the problems in terms of the higher rank numerical ranges of the Choi-Kraus operators of the quantum operations/channels. In this lecture, problems and results involving different kind of numerical ranges will be described. Lecture 3 -- Preserver Problems and Quantum Information Science Preserver problems concern the characterization of maps on matrices or operators with special properties. In connection to quantum information science, researcher are interested in maps that leave invariant some certain measures, relations, or subsets of quantum states or quantum systems. In this lecture, selected problems and results in such research will be described