Note on transmitted complexity for the modified compound states
Note on transmitted complexity for the modified compound states
复制标题
关于修改后的复合状态的传输复杂性的注释
DOI：
10.1142/s0217751x22430230
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发表时间：
2022
影响因子：
1.6
通讯作者：
Noboru Watanabe
中科院分区：
文献类型：
--
作者：
Takahiro Nishiyama;Noboru Watanabe;Noboru Watanabe
在Ref. 27中，Ohya提出了综合多种研究复杂系统的方法的信息动力学。在信息动力学中，复杂性有两种类型，一种是表示系统本身的状态复杂性，另一种是两个系统之间传递的复杂性。经典系统和量子系统中的熵就是这些信息动力学复杂性的例子。传递复杂度是分析通信过程中信息传递效率的重要工具。为了处理动态过程的流动，不仅在经典系统中而且在量子系统中引入了动态熵。基于Accardi在研究量子马尔可夫过程中引入的跃迁期望，在文献17中定义了完全正（CP）映射的KOW熵。由KOW熵构造了广义AOW和AF熵。复合态是定义传递熵的重要工具。利用文献36和文献45中的广义AOW熵定义了与可分离复合状态相关的传输复杂度。本文利用修正复合态定义了传递复杂性（量子动力互熵），并证明了独立量子动力系统传递复杂性的基本不等式。
In Ref. 27, Ohya proposed the information dynamics synthesizing several ways of studying complex systems. In information dynamics, there are two types of complexities, one is a complexity of state representing system itself and another is a transmitted complexity between two systems. Entropies in classical and quantum systems are examples of these complexities of information dynamics. Transmitted complexity is an important tool to analyze the efficiency of information transmission in communication processes. In order to treat a flow of dynamical process, dynamical entropies were introduced in not only classical but also quantum systems.Based on the transition expectation introduced by Accardi to study quantum Markov process, the KOW entropy for completely positive (CP) maps was defined in Ref. 17. The generalized AOW and the AF entropies was constructed by the KOW entropy. The compound states are important tool to define the transmitted entropy43,44. The transmitted complexity associated with the separable compound states is defined by using the generalized AOW entropy in Refs. 36 and 45.In this paper, we define a transmitted complexity (quantum dynamical mutual entropy) by means of the modified compound states and we prove the fundamental inequalities of the transmitted complexity for the independent quantum dynamical systems.