2019/08/06 by Kyouhei Ohmura, Ohmura, Kyouhei, Noboru Watanabe +1
Engineering · Physics and Astronomy · #47L90 #81P45 #Control and Stability of Dynamical Systems #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.1908.01955
openalex publication_date 2019/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The dynamical entropy on von Neumann algebras defined by Accardi, Ohya and Watanabe (AOW entropy) is a natural noncommutative extension of the classical dynamical entropy. On the other hand, quantum spin lattice systems currently used in quantum computing and communication processes are mathematically described by C^*-algebras called CAR algebras. Therefore, in order to obtain the average amount of quantum information and to calculate the uncertainty of the dynamics of quantum spin systems, it is necessary to define dynamical entropy on CAR algebras. In this paper, we formulate dynamical entropy on CAR algebras based on the construction of the AOW entropy. Moreover, we compute the introduced entropy for a 2 × 2 matrix algebra case which has relation to the quantum spin system.