17 research outputs found
Derandomizing Compressed Sensing With Combinatorial Design
Compressed sensing is the art of effectively reconstructing structured n-dimensional vectors from substantially fewer measurements than naively anticipated. A plethora of analytical reconstruction guarantees support this credo. The strongest among them are based on deep results from large-dimensional probability theory and require a considerable amount of randomness in the measurement design. Here, we demonstrate that derandomization techniques allow for a considerable reduction in the randomness required for such proof strategies. More precisely, we establish uniform s-sparse reconstruction guarantees for Cs log(n) measurements that are chosen independently from strength-4 orthogonal arrays and maximal sets of mutually unbiased bases, respectively. These are highly structured families of Än2 vectors that imitate signed Bernoulli and standard Gaussian vectors in a (partially) derandomized fashion.DFG, 414044773, Open Access Publizieren 2019 - 2020 / Technische Universität Berli
Applications of coherent classical communication and the Schur transform to quantum information theory
Quantum mechanics has led not only to new physical theories, but also a new
understanding of information and computation. Quantum information began by
yielding new methods for achieving classical tasks such as factoring and key
distribution but also suggests a completely new set of quantum problems, such
as sending quantum information over quantum channels or efficiently performing
particular basis changes on a quantum computer. This thesis contributes two
new, purely quantum, tools to quantum information theory--coherent classical
communication in the first half and an efficient quantum circuit for the Schur
transform in the second half.Comment: 176 pages. Chapters 1 and 4 are a slightly older version of
quant-ph/0512015. Chapter 2 is quant-ph/0205057 plus unpublished extensions
(slightly outdated by quant-ph/0511219) and chapter 3 is quant-ph/0307091,
quant-ph/0412126 and change. Chapters 5-8 are based on quant-ph/0407082, but
go much furthe