A Simplification Algorithm for Calculation of the Mutual Information by Quantum Combined Measurement

Shogo USAMI   Tsuyoshi Sasaki USUDA   Ichi TAKUMI   Masayasu HATA   

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E82-A   No.10   pp.2185-2190
Publication Date: 1999/10/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Quantum Information
Keyword: 
quantum information theory ,  channel capacity ,  square-root measurement ,  mutual information ,  superadditivity ,  

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Summary: 
Recently, the quantum information theory attracts much attention. In quantum information theory, the existence of superadditivity in capacity of a quantum channel was foreseen conventionally. So far, some examples of codes which show the superadditivity in capacity have been clarified. However in present stage, characteristics of superadditivity are not still clear up enough. The reason is as follows. All examples were shown by calculating the mutual information by quantum combined measurement, so that one had to solve the eigenvalue and the eigenvector problems. In this paper, we construct a simplification algorithm to calculate the mutual information by using square-root measurement as decoding process of quantum combined measurement. The eigenvalue and the eigenvector problems are avoided in the algorithm by using group covariancy of binary linear codes. Moreover, we derive the analytical solution of the mutual information for parity check codes with any length as an example of applying the simplification algorithm.