On Entropic Chaos Degree in a Quantum Dynamical System (Mathematical Study of Quantum Dynamical Systems and Its Application to Quantum Computer)

M. Hossein Partovi

Maeda Michihiro, Masanori Ohya

Kei Inoue, Masanori Ohya, Igor Vasil'evich Volovich

Quantum Baker's map is a theoretical model that exhibits chaos in a quantum system. In this paper, we introduce a combined map by combining several quantum Baker's maps. Chaos of such a combined dynamics is studied by the entropic chaos degree.

Noboru Watanabe, Andrei Yu. Khrennikov

Xi-Hao Fang, Fei Ming, Dong Wang

Uncertainty principle plays a crucial role in quantum mechanics, because it captures the essence of the inevitable randomness associated with the outcomes of two incompatible quantum measurements. Information entropy can perfectly describe this type of randomness in information theory, because entropy can measure the degree of chaos in a given quantum system. However, the quantum-assisted uncertainty of entropy eventually inflate inevitably as the quantum correlations of the system are progressively corrupted by noise from the surrounding environment. In this paper, we investigate the dynamical features of the von Neumann entropic uncertainty in the presence of quantum memory, exploring the time evolution of entropic uncertainty suffer noise from the surrounding. Noteworthily, how the environmental noises affect the uncertainty of entropy is revealed, and specifically we verify how two types of noise environments, AD channel and BPF channel, influence the uncertainty. Meanwhile, we put forward some effective operation strategies to reduce the magnitude of the measurement uncertainty under the open systems. Furthermore, we explore the applications of the uncertainty relation investigated on entanglement witness and quantum channel capacity. Therefore , in open quantum correlation systems, our investigations could provide an insight into quantum measurement estimation

Jincheng Zhang

This paper investigates the intersection of quantum chaos and quantum computing control. It explores the potential influence of chaotic behavior within quantum systems on computational processes and proposes control strategies to mitigate these effects. The core argument centers on the recognition of quantum chaos as a crucial, yet often overlooked, element in the precise control required for reliable quantum computation. Through the application of chaos theory, this work analyzes the manifestation of chaotic dynamics in quantum systems, detailing the implications for qubit stability and gate fidelity. Specific control techniques, including feedback mechanisms and tailored Hamiltonian designs, are examined and discussed, ultimately aiming to harness, rather than suppress, chaotic behavior to potentially enhance certain quantum algorithms. The research contributes to a deeper understanding of the complex relationship between quantum systems and chaos, providing a foundation for the development of more robust and adaptable quantum control protocols. The study utilizes mathematical formalism to rigorously define and analyze the concepts explored, focusing on key equations governing quantum dynamics and chaotic systems.