This book carefully considers the foundational mathematics of adaptive quantum information processing. Quantum information has the potential to revolutionize the information is stored, processed, transferred, and acquired. In particular, quantum information offers exciting new approaches to secure communication, computation, and sensing. However, in order to realize such technologies, it is key to first understand the effects that external systems can induce on a quantum system. The author builds upon recent studies that have explored the underlying structure of quantum information and the effects of qubit channels in quantum communication protocols. This book also explores the fundamental constraints of adaptations as they pertain to the exchange of quantum information, referred to adaptive quantum communication. Readers will gain a well-rounded understanding of error rates for quantum qubit channels as well as a fundamental basis of possible improvements that culminate in physically realizable examples for transmission improvement.