Thermalization and Quantum Information in Conformal Field Theory

The consequences of the constraints of conformal symmetry are far-reaching withintheoretical physics. In this dissertation we address a series of questions in conformalfield theory: 1) We calculate the spectrum of qKdV charges in a large central chargeexpansion. 2) We determine the corrections to bulk information geometry from 1/Ncontributions to holographic correlators. 3) We study the higher genus partitionsfunctions of CFTs associated with classical and quantum error-correcting codes

Algorithms to Exploit Data Sparsity

While data in the real world is very high-dimensional, it generally has some underlying structure; for instance, if we think of an image as a set of pixels with associated color values, most possible settings of color values correspond to something more like random noise than what we typically think of as a picture. With an appropriate transformation of basis, this underlying structure can often be converted into sparsity in data, giving an equivalent representation of the data where the magnitude is large in only a few directions relative to the ambient dimension. This motivates a variety of theoretical questions around designing algorithms that can exploit this data sparsity to achieve better performance than what would be possible naively, and in this thesis we tackle several such questions.We first examine the question of simply approximating the level of sparsity of a signal under several different measurement models, a natural first step if the sparsity is to be exploited by other algorithms. Second, we look at a particular sparse signal recovery problem called nonadaptive probabilistic group testing, and investigate the question of exactly how sparse the signal needs to be before the methods used for recovering sparse signals outperform those used for non-sparse signals. Third, we prove novel upper bounds on the number of measurements needed to recover a sparse signal in the universal one-bit compressed sensing model of sparse signal recovery. Fourth, we give some approximations of an information-theoretic quantity called the index coding rate of a network modeled by a graph, in the special case that the graph is sparse or otherwise highly structured. For each of the problems considered, we also discuss some remaining open questions and conjectures, as well as possible directions towards their solutions

Interim Design Report

The International Design Study for the Neutrino Factory (the IDS-NF) was established by the community at the ninth "International Workshop on Neutrino Factories, super-beams, and beta- beams" which was held in Okayama in August 2007. The IDS-NF mandate is to deliver the Reference Design Report (RDR) for the facility on the timescale of 2012/13. In addition, the mandate for the study [3] requires an Interim Design Report to be delivered midway through the project as a step on the way to the RDR. This document, the IDR, has two functions: it marks the point in the IDS-NF at which the emphasis turns to the engineering studies required to deliver the RDR and it documents baseline concepts for the accelerator complex, the neutrino detectors, and the instrumentation systems. The IDS-NF is, in essence, a site-independent study. Example sites, CERN, FNAL, and RAL, have been identified to allow site-specific issues to be addressed in the cost analysis that will be presented in the RDR. The choice of example sites should not be interpreted as implying a preferred choice of site for the facility

Multi-Photon Entanglement

Major efforts in quantum information science are devoted to the development of methods that are superior to the one of classical information processing, for example the quantum computer or quantum simulations. For these purposes, superposition and entangled states are considered a decisive resource. Furthermore, since the early days of quantum mechanics, entanglement has revealed the discrepancy between the quantum mechanical and the everyday life perception of the physical world. This combination of fundamental science and application-oriented research makes the realization, characterization, and application of entanglement a challenge pursued by many researchers. In this work, the observation of entangled states of polarization encoded photonic qubits is pushed forward in two directions: flexibility in state observation and increase in photon rate. To achieve flexibility two different schemes are developed: setup-based and entanglement-based observation of inequivalent multi-photon states. The setup-based scheme relies on multi-photon interference at a polarizing beam splitter with prior polarization manipulations. It allows the observation of a family of important four-photon entangled states. The entanglement-based scheme exploits the rich properties of Dicke states under particle projections or loss in order to obtain inequivalent multi-photon entangled states. The observed states are characterized using the fidelity and entanglement witnesses. An increase in photon rate is crucial to achieve entanglement of higher photon numbers. This holds especially, when photon sources are utilized that emit photons spontaneously. To this end, a new photon source is presented based on a femtosecond ultraviolet enhancement cavity and applied to the observation of the six-photon Dicke state with three excitations. The implemented schemes not only allow the observation of inequivalent types of entanglement, but also the realization of various quantum information tasks. In this work, the four-photon GHZ state has been used in a quantum simulation of a minimal instance of the toric code. This code enables the demonstration of basic properties of anyons, which are quasiparticles distinct from bosons and fermions. Further, the six-photon Dicke state has been applied for quantum metrology: It allows one to estimate a phase shift with a higher precision than by using only classical resources. Altogether, a whole series of experiments for observing inequivalent multi-photon entangled states can now be substituted by a single experimental setup based on the designs developed in this work. In addition to this new approach of photon processing, a novel photon source has been implemented, paving the way to realizations of applications requiring higher photon numbers.This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the Ludwig-Maximilians-Universität München's products or services. Internal or personal use of this material is permitted. However, permission to reprint republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this material, you agree to all provisions of the copyright laws protecting it