Doctor of Philosophy (PhD)
Physics and Astronomy
This is a two-part thesis glued together by an everlasting theme in Quantum Information Science \-- to save the quantum state, or the information stored in it, from unavoidably environment-induced noise. The first part of this thesis studies the ultimate rate of reliably transmitting information, stored in quantum systems, through a noisy evolution. Specifically, we consider communication over optical links, upon which future inter-city quantum communication networks will be built. We show how to treat the infinite-dimensional bosonic system rigorously and establish the theory of energy-constrained private and quantum communication over quantum channels. Our result represents important progress in the field of energy-constrained quantum communication theory. As an example of communication over optical channels, we solve the triple trade-off capacity and broadcast capacity of quantum-limited amplifier channels. Our result not only includes two single-letter capacities, which are rare in quantum communication theory, but it is also the only known application of a recently proved minimum output-entropy conjecture. The second part of my thesis includes two of my works on dynamical decoupling (DD). DD is an open-loop technique to keep a qubit alive during decoherence, which is important for the actual implementation of quantum memory or a quantum computer. Instead of treating quantum evolution as a completely positive trace preserving map like in communication theory, we consider time-dependent evolution of a specific quantum system in quantum control theory. With more than decade of development of the theory of DD, people started to focus on pulse sequences with low sequencing complexity (called digital pulse sequences), which are required for large-scale implementation of quantum computation devices. We propose two unifying frameworks to systematically generate these engineering-friendly pulse sequences. Surprisingly, we prove that these two frameworks are actually two sides of the same coin, and thus our work greatly deepens our understanding of the underlying structure and the decoupling performance of digital pulse sequences.
Qi, Haoyu, "Energy-Constrained Quantum Communication and Digital Dynamical Decoupling" (2017). LSU Doctoral Dissertations. 4131.