Adaptive Dynamics and Its Applications to Chaos and NPC Problem Quantum Algorithm for SAT Problem and Quantum Mutual Entropy New Quantum Algorithm for Studying NP-Complete Problems Entanglement, Quantum Entropy and Mutual Information Fundamentals of Quantum Mutual Entropy and Capacity Compound Channels, Transition Expectations, and Liftings Complexities and Their Applications to Characterization of Chaos Complexity, Fractal Dimension for Quantum States Information Dynamics and Its Applications to Optical Communication Processes Information Theoretical Treatments of Genes Some Aspects of Quantum Information Theory and Their Applications to Irreversible Processes On Compound State and Mutual Information in Quantum Information Theory Note on Quantum Probability Quantum Ergodic Channels in Operator Algebras On Open System Dynamics -- An Operator Algebraic Study Dynamical Process in Linear Response Theory Stability of Weiss Ising Model and other papers.
Symmetry principles have played a crucial role in the development of modern physics and underpin our most fundamental theories of nature. The present thesis is concerned with the analysis of symmetries in the context of quantum information theory. Whenever a quantum mechanical system interacts with its environment it is subjected to decoherence, a process that is typically irreversible and most generally treated abstractly using the concept of quantum operations. If there is an underlying symmetry principle, additional structures emerge. The central question we address is, What are the consequences of global or local gauge symmetry on the structure of many-body quantum processes?This leads us to a diagrammatic framework of decomposing quantum operations into terms that respond to the symmetry principle in particular ways and respect the causal structures involved. We present two core applications. First, we address the interplay between irreversibility and repeatable use of coherent resources under symmetry constraints. Second, we give an information-theoretic perspective on gauging globally symmetric dynamics to a local symmetry applicable even in the presence of irreversibility and thus it goes beyond the usual Lagrangian formulation. Finally, we analyse the departure from conservation laws under symmetric dynamics subject to decoherence.