Quantum information has the potential to revolutionize the way we store, process, transfer and acquire information [1,14,15,21,37]. In particular, quantum information offers exciting new approaches to secure communication, computation and sensing. However, in order to realize such technologies, we must first understand the effect that environmental noise has on a quantum system. This dissertation builds upon recent studies that have explored the underlying structure of quantum information and the effects of qubit channels in quantum communication protocols. This work is divided into five main chapters, with Chapter 1 being a brief introduction to quantum information. We then begin Chapter 2 by defining the error function for our qubit communication protocols. From there we explore the properties of our error functions and the topological space that they form. In Chapter 3 we consider the newly patented process Adaptive Quantum Information Processing, patent number US9838141 B2; originally outlined by Martin in . We restate the adaptive scheme and exemplify its application through the Prepare and Send Protocol and Quantum Key Distribution. Applying our results from Chapter 2, we obtain an expression for the adaptability of unital channels in these two protocols and classify the channels that admit the most improvement. We dedicate Chapter 4 to the derivation of gravitational noise, and show that in certain circumstances gravity results in a channel that can be maximally improved in Adaptive QKD [3,14,16]. Lastly, we study the set of error functions through the lens of domain theory. Domain theory is a subset of mathematics that was developed in order to rigorously formalize computations. The first four chapters are all consequences of past discoveries in the mathematical structure of quantum channels. In Chapter 5 we characterize the set of error functions through domain theory, extending the mathematical foundations of quantum information. [12,18,20, 22, 23,25].
Doctor of Philosophy (Ph.D.)
College of Sciences
Length of Campus-only Access
Doctoral Dissertation (Open Access)
Bonior, Daniel, "Mathematical Foundations of Adaptive Quantum Processing" (2018). Electronic Theses and Dissertations, 2004-2019. 6173.