首页 | 本学科首页   官方微博 | 高级检索  
     检索      


Simplification of the Gram Matrix Eigenvalue Problem for Quadrature Amplitude Modulation Signals
Authors:Ryusuke Miyazaki  Tiancheng Wang  Tsuyoshi Sasaki Usuda
Institution:1.Graduate School of Information Science and Technology, Aichi Prefectural University, Nagakute 480-1198, Aichi, Japan;2.Faculty of Engineering, Kanagawa University, Yokohama 221-8686, Kanagawa, Japan
Abstract:In quantum information science, it is very important to solve the eigenvalue problem of the Gram matrix for quantum signals. This allows various quantities to be calculated, such as the error probability, mutual information, channel capacity, and the upper and lower bounds of the reliability function. 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 that must be used, rendering the computations inefficient. Recently, we have shown that, for asymmetric signals such as amplitude-shift keying coherent-state signals, the Gram matrix eigenvalue problem can be simplified by exploiting its partial symmetry. In this paper, we clarify a method for simplifying the eigenvalue problem of the Gram matrix for quadrature amplitude modulation (QAM) signals, which are extremely important for applications in quantum communication and quantum ciphers. The results presented in this paper are applicable to ordinary QAM signals as well as modified QAM signals, which enhance the security of quantum cryptography.
Keywords:quantum communication  quantum cipher  quadrature amplitude modulation (QAM)  coherent state  Gram matrix  square-root measurement (SRM)
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号