2010/06/24 by Vlad Gheorghiu, Gheorghiu, Vlad
Computer Science · Mathematics · Physics and Astronomy · #Bipartite graph #Combinatorics #Computer science #Curse of dimensionality #Discrete mathematics #FOS: Physical sciences #Graph #Mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum entanglement #Separable space #Separable state #Theoretical computer science #quant-ph
paper · pdf · doi:10.48550/arxiv.1006.4888
published in arXiv (Cornell University) (Cornell University) · 106 pages, LaTeX. Carnegie Mellon University PhD Thesis, Quantum Information Theory
arxiv created 2010/06/24 · openalex publication_date 2010/06/24 · arxiv updated 2010/06/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In the first part of this Dissertation, I study the differences between LOCC (local operations and classical communication) and the more general class of separable operations. I show that the two classes coincide for the case of pure bipartite state input, and derive a set of important consequences. Using similar techniques I also generalize the no-cloning theorem when restricted to separable operations and show that cloning becomes much more restrictive, by providing necessary (and sometimes sufficient) conditions. In the second part I investigate graph states and graph codes with carrier qudits of arbitrary dimensionality, and extend the notion of stabilizer to any dimension, not necessarily prime. I further study how and where information is located in the various subsets of the qudit carriers of arbitrary additive graph codes, and provide efficient techniques that can be used in deciding what types of information a subset contains.