PhD Thesis Presentation: Hybrid Quantum Systems: Complementarity of Quantum Privacy and Error-Correction, and Higher Rank Matricial Ranges

PhD Candidate

Mike Ignatius Nelson

Abstract

The idea to transmit classical bits simultaneously with quantum information over a quantum channel has been explored since near the beginning of research in quantum information theory and computation fields. The process described, which we refer to as hybrid quantum computing, has been examined first with purely information theoretic considerations, and then later demonstrated to have benefits over using independent channels. The subject since lay mostly dormant, until more recent work demonstrating the existence of good hybrid quantum error codes, as well as generalized mathematical results in the structure of error correcting codes.  

In this thesis, I outline contributions to understanding criterion for the existence of hybrid codes, natural extensions of quantum computing ideas to the hybrid case as well as demonstrate some interesting practical examples. The thesis is organized in three [or four] main parts. The first considers the subject of the complementary relationship between quantum privacy and error correction in hybrid computing scenarios. Next, I extend these ideas to the approximate cases. Finally we see the introduction of higher rank matricial ranges as a tool to ascertain the existence of hybrid codes and benchmark the hybrid capacity of quantum channels. 

Examination Committee

• Dr. Ralf Gellert, Chair 
• Dr. David Kribs, Advisor 
• Dr. Bei Zeng, Co-Advisor 
• Dr. Rajesh Pereira 
• Dr. Jon Yard, External Examiner (University of Waterloo)