Watanabe Noboru
Department of Information Sciences, Tokyo University of Science, Noda City, Chiba 278-8510, Japan.
Entropy (Basel). 2020 Mar 5;22(3):298. doi: 10.3390/e22030298.
It has been shown that joint probability distributions of quantum systems generally do not exist, and the key to solving this concern is the compound state invented by Ohya. The Ohya compound state constructed by the Schatten decomposition (i.e., one-dimensional orthogonal projection) of the input state shows the correlation between the states of the input and output systems. In 1983, Ohya formulated the quantum mutual entropy by applying this compound state. Since this mutual entropy satisfies the fundamental inequality, one may say that it represents the amount of information correctly transmitted from the input system through the channel to the output system, and it may play an important role in discussing the efficiency of information transfer in quantum systems. Since the Ohya compound state is separable state, it is important that we must look more carefully into the entangled compound state. This paper is intended as an investigation of the construction of the entangled compound state, and the hybrid entangled compound state is introduced. The purpose of this paper is to consider the validity of the compound states constructing the quantum mutual entropy type complexity. It seems reasonable to suppose that the quantum mutual entropy type complexity defined by using the entangled compound state is not useful to discuss the efficiency of information transmission from the initial system to the final system.
已经表明，量子系统的联合概率分布通常不存在，解决这一问题的关键是大矢发明的复合态。通过输入态的沙滕分解（即一维正交投影）构建的大矢复合态显示了输入和输出系统状态之间的相关性。1983年，大矢通过应用这种复合态提出了量子互熵。由于这种互熵满足基本不等式，可以说它代表了从输入系统通过信道正确传输到输出系统的信息量，并且它可能在讨论量子系统中信息传递的效率方面发挥重要作用。由于大矢复合态是可分态，我们必须更仔细地研究纠缠复合态。本文旨在研究纠缠复合态的构造，并引入了混合纠缠复合态。本文的目的是考虑构建量子互熵型复杂度的复合态的有效性。假设使用纠缠复合态定义的量子互熵型复杂度对于讨论从初始系统到最终系统的信息传输效率没有用处似乎是合理的。
