扇形領域の信号点を回転してできる量子信号のグラム行列固有値問題の簡単化

カテゴリ: 論文誌(論文単位)

グループ名: 【C】電子・情報・システム部門

発行日: 2022/12/01

タイトル(英語): Simplification of the Gram Matrix Eigenvalue Problem for Quantum Signals Formed by Rotating Signal Points in a Circular Sector Region

著者名: 王　天澄（神奈川大学 工学部／愛知県立大学大学院 情報科学研究科），宮崎　龍輔（愛知県立大学大学院 情報科学研究科），高比良　宗一（愛知県立大学大学院 情報科学研究科／大阪大学大学院 基礎工学研究科），臼田　毅（愛知県立大学大学院 情報科学研究科）

著者名(英語): Tiancheng Wang (Faculty of Engineering, Kanagawa University/Graduate School of Information Science and Technology, Aichi Prefectural University), Ryusuke Miyazaki (Graduate School of Information Science and Technology, Aichi Prefectural University), Souichi Takahira (Graduate School of Information Science and Technology, Aichi Prefectural University/Graduate School of Engineering Science, Osaka University), Tsuyoshi Sasaki Usuda (Graduate School of Information Science and Technology, Aichi Prefectural University)

キーワード: 量子通信，グラム行列，square-root measurement，amplitude phase shift keying_x000D_　　quantum communication，Gram matrix，square-root measurement，amplitude phase shift keying

要約(英語): Efficient computation of eigenvalues and eigenvectors of the Gram matrix for quantum signals is desirable in the field of quantum communication theory. Because various quantities such as the error probability, mutual information, channel capacity, and upper and lower bounds of the reliability function can be obtained by the eigenvalues and eigenvectors. Moreover, solving the eigenvalue problem also provides a matrix representation of quantum signals, which is useful for simulating quantum systems. In the case of symmetric signals, analytic solutions to the eigenvalue problem of the Gram matrix have been obtained and efficient computations are possible. However, for asymmetric signals, there is no analytic solution and universal numerical algorithms must be used. Recently, we have shown that, for certain asymmetric signals, the Gram matrix eigenvalue problem can be simplified and it is sufficient to consider the eigenvalue problem of smaller matrices at half or quarter size. In this paper, we consider nm-ary quantum signals formed by rotating signal points in a circular sector region and show that solving the 1/n-size matrix eigenvalue problem is sufficient to give the eigenvalues and eigenvectors of the Gram matrix.

本誌: 電気学会論文誌C（電子・情報・システム部門誌） Vol.142 No.12 （2022） 特集：電気・電子・情報関係学会東海支部連合大会

本誌掲載ページ: 1253-1261 p

原稿種別: 論文／日本語

電子版へのリンク: https://www.jstage.jst.go.jp/article/ieejeiss/142/12/142_1253/_article/-char/ja/