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Special Seminar in Quantum Information - What are quantum channels through my old dream?


In 1970, I started off my adventure in the mathematical wonderland of completely positive linear maps (alias, quantum channels).  Now, I am awaken to the new era of quantum computers, with all sorts of information processes in the setting of non-commutative analysis.  As the time runs backwards in an alternating world through the looking glass, I have to come back to the same old scene to release myself from quantum entanglements.  In particular, I shall give a MODERN report on my 1975 paper (Completely positive linear maps on complex matrices, Linear Algebra Appl. 10 (1975), pp. 285-290) which has been cited in more than 500 recent research articles (as shown in Google Scholars of March 2011).

This is an expository talk in the simple language of  mathematics; no background knowledge of information theory will be assumed for this talk.