Stabilized Distance Measures and Quantum Error Correction


Quantum information theory is a quickly-growing area of research that presents no shortage of mathematical challenges. In this thesis, two basic analytic and algebraic problems of interest in quantum information are considered. The first problem considered is that of computing a crucial distance measure for linear maps on finite-dimensional Hilbert space, given by the the diamond and completely bounded norms of differences of quantum operations. Based on the theory of completely bounded maps, an algorithm to compute the diamond and completely bounded norms of arbitrary linear maps is formulated and presented. The algorithm is applied to derive a new proof and formula for the distance between arbitrary unitary maps. Finally, an implementation of the algorithm via MATLAB is presented, and its efficiency is discussed. Attention is next turned to quantum error correction, where a new algebraic characterization of error-correcting codes is derived. These results are used to explicitly compute a correction operation, and a new characterization of correctable subsystems in terms of representation theory is obtained.


  • Nathaniel Johnston


Cite as:

  • N. Johnston. Stabilized Distance Measures and Quantum Error Correction. Master’s thesis, University of Guelph, 2008.

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  1. Zahra
    December 2nd, 2013 at 17:07 | #1

    Dear Nathaniel,
    I’m Master student in the field of Telecommunication system engineering. It’s about a year that I’m working on
    ARQ schemes in MIMO systems and Error correction and detection methods. While I was searching in internet I found your thesis and I wanne say thank you for sharing your thesis and the result of your studies. Also if it’s not bothering I would like to be in touch with you if I had some questions.
    Zahra Zareei

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