Investigation on Error-Correcting Codes Based on Quantum Theory and Its Applications to Information Security Issues

2014 Fiscal Year Final Research Report

• Project/Area Number: 22540150
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Tamagawa University
• Principal Investigator: HAMADA Mitsuru 玉川大学, 量子情報科学研究所, 教授 (10407679)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 符号理論 / 誤り訂正符号 / 線形代数 / アルゴリズム / 量子論 / 量子コンピュータ / 情報基礎 / SU(2)

Outline of Final Research Achievements

Quotient codes, which generalize classical error-correcting codes and are applicable to quantum error correction, were studied. The present study was mainly aimed at embodiment of concatenated quotient codes, which are proposed by this researcher, refined performance analysis of them, and exploration into related issues. For instance, while this researcher had proved the asymptotic optimality of the proposed concatenated codes used on wiretap channels (a model due to Wyner) around the time of the application of this research, he obtained related results during the research period of the Kakenhi. In the latter half of the period, he proposed a construction method for arbitrary quantum information processing on single-qubit systems (specifically, arbitrary SU(2) elements). This is also a concrete constructive (algorithmic) method regarding information processing , and its optimality was also proved rigorously by himself.

Free Research Field

応用数学