Tesi sul tema "Information theory"
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Hjørland, Birger. "Principia Informatica. Foundational Theory of Information and Principles of Information Services". Libraries Unlimited, 2002. http://hdl.handle.net/10150/105735.
Testo completoBond, Rachael Louise. "Relational information theory". Thesis, University of Sussex, 2018. http://sro.sussex.ac.uk/id/eprint/76664/.
Testo completoSahai, Anant. "Anytime information theory". Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/8770.
Testo completoIncludes bibliographical references (p. 171-175).
We study the reliable communication of delay-sensitive bit streams through noisy channels. To bring the issues into sharp focus, we will focus on the specific problem of communicating the values of an unstable real-valued discrete-time Markov random process through a finite capacity noisy channel so as to have finite average squared error from end-to-end. On the source side, we give a coding theorem for such unstable processes that shows that we can achieve the rate-distortion bound even in the infinite horizon case if we are willing to tolerate bounded delays in encoding and decoding. On the channel side, we define a new parametric notion of capacity called anytime capacity that corresponds to a sense of reliable transmission that is stronger than the traditional Shannon capacity sense but is less demanding than the sense underlying zero-error capacity. We show that anytime capacity exists for memoryless channels without feedback and is connected to standard random coding error exponents. The main result of the thesis is a new source/channel separation theorem that encompasses unstable processes and establishes that the stronger notion of anytime capacity is required to be able to deal with delay-sensitive bit streams. This theorem is then applied in the control systems context to show that anytime capacity is also required to evaluate channels if we intend to use them as part of a feedback link from sensing to actuation. Finally, the theorem is used to shed light on the concept of "quality of service requirements" by examining a toy mathematical example for which we prove the absolute necessity of differentiated service without appealing to human preferences.
by Anant Sahai.
Ph.D.
Schumann, Robert Helmut. "Quantum information theory". Thesis, Stellenbosch : Stellenbosch University, 2000. http://hdl.handle.net/10019.1/51892.
Testo completoENGLISH ABSTRACT: What are the information processing capabilities of physical systems? As recently as the first half of the 20th century this question did not even have a definite meaning. What is information, and how would one process it? It took the development of theories of computing (in the 1930s) and information (late in the 1940s) for us to formulate mathematically what it means to compute or communicate. Yet these theories were abstract, based on axiomatic mathematics: what did physical systems have to do with these axioms? Rolf Landauer had the essential insight - "Information is physical" - that information is always encoded in the state of a physical system, whose dynamics on a microscopic level are well-described by quantum physics. This means that we cannot discuss information without discussing how it is represented, and how nature dictates it should behave. Wigner considered the situation from another perspective when he wrote about "the unreasonable effectiveness of mathematics in the natural sciences". Why are the computational techniques of mathematics so astonishingly useful in describing the physical world [1]? One might begin to suspect foul play in the universe's operating principles. Interesting insights into the physics of information accumulated through the 1970s and 1980s - most sensationally in the proposal for a "quantum computer". If we were to mark a particular year in which an explosion of interest took place in information physics, that year would have to be 1994, when Shor showed that a problem of practical interest (factorisation of integers) could be solved easily on a quantum computer. But the applications of information in physics - and vice versa - have been far more widespread than this popular discovery. These applications range from improved experimental technology, more sophisticated measurement techniques, methods for characterising the quantum/classical boundary, tools for quantum chaos, and deeper insight into quantum theory and nature. In this thesis I present a short review of ideas in quantum information theory. The first chapter contains introductory material, sketching the central ideas of probability and information theory. Quantum mechanics is presented at the level of advanced undergraduate knowledge, together with some useful tools for quantum mechanics of open systems. In the second chapter I outline how classical information is represented in quantum systems and what this means for agents trying to extract information from these systems. The final chapter presents a new resource: quantum information. This resource has some bewildering applications which have been discovered in the last ten years, and continually presents us with unexpected insights into quantum theory and the universe.
AFRIKAANSE OPSOMMING: Tot watter mate kan fisiese sisteme informasie verwerk? So onlangs soos die begin van die 20ste eeu was dié vraag nog betekenisloos. Wat is informasie, en wat bedoel ons as ons dit wil verwerk? Dit was eers met die ontwikkeling van die teorieë van berekening (in die 1930's) en informasie (in die laat 1940's) dat die tegnologie beskikbaar geword het wat ons toelaat om wiskundig te formuleer wat dit beteken om te bereken of te kommunikeer. Hierdie teorieë was egter abstrak en op aksiomatiese wiskunde gegrond - mens sou wel kon wonder wat fisiese sisteme met hierdie aksiomas te make het. Dit was Rolf Landauer wat uiteindelik die nodige insig verskaf het - "Informasie is fisies" - informasie word juis altyd in 'n fisiese toestand gekodeer, en so 'n fisiese toestand word op die mikroskopiese vlak akkuraat deur kwantumfisika beskryf. Dit beteken dat ons nie informasie kan bespreek sonder om ook na die fisiese voorstelling te verwys nie, of sonder om in ag te neem nie dat die natuur die gedrag van informasie voorskryf. Hierdie situasie is vanaf 'n ander perspektief ook deur Wigner beskou toe hy geskryf het oor "die onredelike doeltreffendheid van wiskunde in die natuurwetenskappe". Waarom slaag wiskundige strukture en tegnieke van wiskunde so uitstekend daarin om die fisiese wêreld te beskryf [1]? Dit laat 'n mens wonder of die beginsels waarvolgens die heelal inmekaar steek spesiaal so saamgeflans is om ons 'n rat voor die oë te draai. Die fisika van informasie het in die 1970's en 1980's heelwat interessante insigte opgelewer, waarvan die mees opspraakwekkende sekerlik die gedagte van 'n kwantumrekenaar is. As ons één jaar wil uitsonder as die begin van informasiefisika, is dit die jaar 1994 toe Shor ontdek het dat 'n belangrike probleem van algemene belang (die faktorisering van groot heelgetalle) moontlik gemaak word deur 'n kwantumrekenaar. Die toepassings van informasie in fisika, en andersom, strek egter veel wyer as hierdie sleutel toepassing. Ander toepassings strek van verbeterde eksperimentele metodes, deur gesofistikeerde meetmetodes, metodes vir die ondersoek en beskrywing van kwantumchaos tot by dieper insig in die samehang van kwantumteorie en die natuur. In hierdie tesis bied ek 'n kort oorsig oor die belangrikste idees van kwantuminformasie teorie. Die eerste hoofstuk bestaan uit inleidende materiaal oor die belangrikste idees van waarskynlikheidsteorie en klassieke informasie teorie. Kwantummeganika word op 'n gevorderde voorgraadse vlak ingevoer, saam met die nodige gereedskap van kwantummeganika vir oop stelsels. In die tweede hoofstuk spreek ek die voorstelling van klassieke informasie en kwantumstelsels aan, en die gepaardgaande moontlikhede vir 'n agent wat informasie uit sulke stelsels wil kry. Die laaste hoofstuk ontgin 'n nuwe hulpbron: kwantuminformasie. Gedurende die afgelope tien jaar het hierdie nuwe hulpbron tot verbysterende nuwe toepassings gelei en ons keer op keer tot onverwagte nuwe insigte oor kwantumteorie en die heelal gelei.
Huang, Shao-Lun Ph D. Massachusetts Institute of Technology. "Euclidean network information theory". Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/84888.
Testo completoCataloged from PDF version of thesis.
Includes bibliographical references (pages 121-123).
Many network information theory problems face the similar difficulty of single letterization. We argue that this is due to the lack of a geometric structure on the space of probability distributions. In this thesis, we develop such a structure by assuming that the distributions of interest are all close to each other. Under this assumption, the Kullback-Leibler (K-L) divergence is reduced to the squared Euclidean metric in an Euclidean space. In addition, we construct the notion of coordinate and inner product, which will facilitate solving communication problems. We will present the application of this approach to the point-to-point channels, general broadcast channels (BC), multiple access channels (MAC) with common sources, interference channels, and multi-hop layered communication networks without or with feedback. It can be shown that with this approach, information theory problems, such as the single-letterization, can be reduced to some linear algebra problems. Solving these linear algebra problems, we will show that for the general broadcast channels, transmitting the common message to receivers can be formulated as the trade-off between linear systems. We also provide an example to visualize this trade-off in a geometric way. For the MAC with common sources, we observe a coherent combining gain due to the cooperation between transmitters, and this gain can be obtained quantitively by applying our technique. In addition, the developments of the broadcast channels and multiple access channels suggest a trade-off relation between generating common messages for multiple users and transmitting them as the common sources to exploit the coherent combining gain, when optimizing the throughputs of communication networks. To study the structure of this trade-off and understand its role in optimizing the network throughput, we construct a deterministic model by our local approach that captures the critical channel parameters and well models the network. With this deterministic model, for multi-hop layered networks, we analyze the optimal network throughputs, and illustrate what kinds of common messages should be generated to achieve the optimal throughputs. Our results provide the insight of how users in a network should cooperate with each other to transmit information efficiently.
by Shao-Lun Huang.
Ph.D.
Faghfoor, Maghrebi Mohammad. "Information gain in quantum theory". Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/2724.
Testo completoVedral, Vlatko. "Quantum information theory of entanglement". Thesis, Imperial College London, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299786.
Testo completoGirolami, Davide. "Quantum correlations in information theory". Thesis, University of Nottingham, 2013. http://eprints.nottingham.ac.uk/13397/.
Testo completoHawes, Vanessa Lucey. "Music's experiment with information theory". Thesis, University of East Anglia, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.514351.
Testo completoDaemi, M. F. "Information theory and pattern recognition". Thesis, University of Nottingham, 1990. http://eprints.nottingham.ac.uk/14003/.
Testo completoButterley, Paul. "Topics in quantum information theory". Thesis, University of York, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.444697.
Testo completoSvensson, Bolennarth. "Information theory in quality engineering". Thesis, University of Strathclyde, 1998. http://digitool.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=29903.
Testo completoAngelino, Cesario Vicenzo. "Information theory oriented image restauration". Nice, 2011. http://www.theses.fr/2011NICE4044.
Testo completoThis thesis addresses informational formulation of image processing problems. This formulation expresses the solution through a minimization of an information-based energy. These energies belong to the nonparametric class in that they do not make any parametric assumption on the underlying data distribution. Energies are expressed directly as a function of the data considered as random variables. However, classical nonparametric estimation relies on fixed-size kernels which becomes less reliable when dealing with high dimensional data. Actually, recent trends in image processing rely on patch-based approaches which deal with vectors describing local patterns of natural images, e. G. , local pixel neighborhoods. The k-Nearest Neighbors framework solves these difficulties by locally adapting the data distribution in such high dimensional spaces. Based on these premises, we develop new algorithms tackling mainly two problems of image processing: deconvolution and denoising. The problem of denoising is developed in the additive white Gaussian noise (AWGN) hypothesis and successively adapted to no AWGN realm such as digital photography and SAR despeckling. The denoising scheme is also modified to propose an inpainting algorithm
Abeyesinghe, Anura Yamesh Preskill John P. "Unification of quantum information theory /". Diss., Pasadena, Calif. : Caltech, 2006. http://resolver.caltech.edu/CaltechETD:etd-05252006-222551.
Testo completoPachas, Erik W. "Probabilistic Methods In Information Theory". CSUSB ScholarWorks, 2016. https://scholarworks.lib.csusb.edu/etd/407.
Testo completoFukuda, Motohisa. "Additivity conjectures in quantum information theory". Thesis, University of Cambridge, 2007. https://www.repository.cam.ac.uk/handle/1810/252051.
Testo completoLukits, Stefan Hermann. "Information theory and partial belief reasoning". Thesis, University of British Columbia, 2016. http://hdl.handle.net/2429/58193.
Testo completoArts, Faculty of
Philosophy, Department of
Graduate
Karvovskaya, Lena, Vadim Kimmelman, Christine Tanja Röhr, Pepi Stavropoulou, Elena Titov e Putten Saskia van. "Information structure : empirical perspectives on theory". Universität Potsdam, 2013. http://opus.kobv.de/ubp/volltexte/2013/6480/.
Testo completoBuchanan, Steven. "The information audit: theory versus practice". Thesis, University of Strathclyde, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.488844.
Testo completoMaroney, Owen Jack Ernest. "Information and entropy in quantum theory". Thesis, Birkbeck (University of London), 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.268835.
Testo completoSørngård, Bård. "Information Theory for Analyzing Neural Networks". Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for datateknikk og informasjonsvitenskap, 2014. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-26773.
Testo completoSchein, Brett E. (Brett Eric). "Distributed coordination in network information theory". Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/16786.
Testo completoIncludes bibliographical references (p. 227-231).
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Constructing a large-scale wireless data network is spectacularly expensive. It is therefore important to understand how to efficiently utilize the physical infrastructure and available battery power, which are expensive system resources. Unfortunately, we currently understand very little about efficient communication in a distributed environment. In distributed wireless networks, there appears to be an interesting and complex trade-off between trying to take advantage of independent noisy signals at different relays and closely coordinating relay transmissions to a receiver. Designing the right structure for efficient communication, by choice of source transmission codebook and relay terminal processing, is the important and difficult problem on which we focus. We use an information theoretic framework to study several very simple multiple terminal networks, focusing exclusively on single source, single destination networks where communication must take place through intermediate nodes. Our goal is to determine how much data we can get reliably from source to destination, placing no importance on delay or computational complexity. The core problem then involves distributed detection at the intermediate nodes and coordination in relaying information to the destination.
by Brett E. Schein.
Ph.D.
Meznaric, Sebastian. "Information theoretic resources in quantum theory". Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:ac3a801c-6351-4882-b6ed-5b2f635cff45.
Testo completoJenkinson, Justin. "Convex Geometric Connections to Information Theory". Case Western Reserve University School of Graduate Studies / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=case1365179413.
Testo completoBenešová, Anita. "Job Information Networks and Game Theory". Master's thesis, Vysoká škola ekonomická v Praze, 2010. http://www.nusl.cz/ntk/nusl-81886.
Testo completoChli, Margarita. "Applying information theory to efficient SLAM". Thesis, Imperial College London, 2010. http://hdl.handle.net/10044/1/5634.
Testo completoHan, Lin. "Graph generative models from information theory". Thesis, University of York, 2012. http://etheses.whiterose.ac.uk/3726/.
Testo completoFallis, Don. "Epistemic Value Theory and Information Ethics". Springer, 2004. http://hdl.handle.net/10150/105254.
Testo completoBonev, Boyan. "Feature selection based on information theory". Doctoral thesis, Universidad de Alicante, 2010. http://hdl.handle.net/10045/18362.
Testo completoIn this thesis we propose a feature selection method for supervised classification. The main contribution is the efficient use of information theory, which provides a solid theoretical framework for measuring the relation between the classes and the features. Mutual information is considered to be the best measure for such purpose. Traditionally it has been measured for ranking single features without taking into account the entire set of selected features. This is due to the computational complexity involved in estimating the mutual information. However, in most data sets the features are not independent and their combination provides much more information about the class, than the sum of their individual prediction power.
Methods based on density estimation can only be used for data sets with a very high number of samples and low number of features. Due to the curse of dimensionality, in a multi-dimensional feature space the amount of samples required for a reliable density estimation is very high. For this reason we analyse the use of different estimation methods which bypass the density estimation and estimate entropy directly from the set of samples. These methods allow us to efficiently evaluate sets of thousands of features.
For high-dimensional feature sets another problem is the search order of the feature space. All non-prohibitive computational cost algorithms search for a sub-optimal feature set. Greedy algorithms are the fastest and are the ones which incur less overfitting. We show that from the information theoretical perspective, a greedy backward selection algorithm conserves the amount of mutual information, even though the feature set is not the minimal one.
We also validate our method in several real-world applications. We apply feature selection to omnidirectional image classification through a novel approach. It is appearance-based and we select features from a bank of filters applied to different parts of the image. The context of the task is place recognition for mobile robotics. Another set of experiments are performed on microarrays from gene expression databases. The classification problem aims to predict the disease of a new patient. We present a comparison of the classification performance and the algorithms we present showed to outperform the existing ones. Finally, we succesfully apply feature selection to spectral graph classification. All the features we use are for unattributed graphs, which constitutes a contribution to the field. We also draw interesting conclusions about which spectral features matter most, under different experimental conditions. In the context of graph classification we also show important is the precise estimation of mutual information and we analyse its impact on the final classification results.
Culpepper, Sarah Elizabeth. "Musical time and information theory entropy". Thesis, University of Iowa, 2010. https://ir.uiowa.edu/etd/659.
Testo completoLaw, Yan Tai. "Pricing under random information flow and the theory of information pricing". Thesis, Imperial College London, 2012. http://hdl.handle.net/10044/1/9292.
Testo completoSadok, Djamel Fawzi Hadj. "Interpersonal interchange of multimedia information". Thesis, University of Kent, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.278242.
Testo completoEsmer, Ozcan. "Information Theory, Entropy And Urban Spatial Structure". Phd thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12606319/index.pdf.
Testo completos Information Gain measures for population changes during the two decades. Empirical findings for Spatial Entropy measures show that overall Ankara-1970 and 1990 density distributions are &lsquo
&rsquo
Uneven&rsquo
&rsquo
and the uniform distribution hypothesis is not confirmed. These measures also indicate a tendency towards &ldquo
More Uniformity&rdquo
for density distributions in comparison to 1970. Information Gain measure for population changes also deviates from zero and direct proportionality hypothesis between posterior 1990 and prior 1970 population distributions by zones is not confirmed. Current research is focused on information processing with more engagement in the urban spatial structure and human behavior. This thesis aims to participate with these efforts and concludes that Information Theory has the potential to generate new profound changes in urban planning and modelling processes.
Puhakainen, P. (Petri). "A design theory for information security awareness". Doctoral thesis, University of Oulu, 2006. http://urn.fi/urn:isbn:9514281144.
Testo completoSeabrooke, Kevin Christopher. "Multimodal brain volume registration using information theory". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/MQ56364.pdf.
Testo completoSavov, Ivan. "Network information theory for classical-quantum channels". Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=110349.
Testo completoLa théorie de l'information multipartite étudie les problèmes de communication avec plusieurs émetteurs, plusieurs récepteurs et des stations relais. L'objectif de cette thèse est d'étendre les idées centrales de la théorie de l'information classique à l'étude des canaux quantiques. Nous allons nous intéresser aux scénarios de communication suivants: les canaux quantiques à accès multiples, les canaux quantiques à interférence, les canaux quantiques de diffusion et les canaux quantiques à relais. Dans chacun des ces scénarios de communication, nous caractérisons les taux de communication réalisables pour l'envoi d'information classique sur ces canaux quantiques. La modélisation quantique des canaux de communication est importante car elle fournit une représentation plus précise de la capacité du canal à transmettre l'information. En utilisant des modèles physiquement réalistes pour les sorties du canal et la procédure de détection, nous obtenons de meilleurs taux de communication que ceux obtenus dans un modèle classique. En effet, l'utilisation de mesures quantiques collectives sur l'ensemble des systèmes physiques en sortie du canal permet une meilleure extraction d'information que des mesures indépendantes sur chaque sous-système. Nous avons choisi d'étudier les canaux à entrée classique et sortie quantique qui constituent une abstraction utile pour l'étude de canaux quantiques généraux où l'encodage est restreint au domaine classique.Nous étudions le régime asymptotique où de nombreuses copies de du canal sont utilisées en parallèle, et les utilisations sont indépendantes. Dans ce contexte, il est possible de caractériser les limites absolues sur la transmission d'information d'un canal, si on connait les statistiques du bruit sur ce canal. Ces résultats théoriques peuvent être utilisées comme un point de repère pour évaluer la performance des protocoles de communication pratiques. Nous considérons surtout les canaux où les sorties sont des systèmes quantiques de dimension finie, analogues aux canaux classiques discrets. Le dernier chapitre présente des applications pratiques de nos résultats à la communication optique, où systèmes physiques auront des degrés de liberté continus. Ce contexte est analogue aux canaux classiques avec bruit gaussien.
Quinn, Kathleen Anne Sara. "Combinatorial structures with applications to information theory". Thesis, Royal Holloway, University of London, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.261791.
Testo completoBarrett, J. "Entanglement, non-locality and quantum information theory". Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.596412.
Testo completoRichardson, Sandra. "HEALTHCARE INFORMATION SYSTEMS:DESIGN THEORY, PRINCIPLES AND APPLICATION". Doctoral diss., University of Central Florida, 2006. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3182.
Testo completoPh.D.
Department of Management Information Systems
Business Administration
Business Administration: Ph.D.
Selig, Marco. "Information theory based high energy photon imaging". Diss., Ludwig-Maximilians-Universität München, 2015. http://nbn-resolving.de/urn:nbn:de:bvb:19-178899.
Testo completoGoyal, Philip. "An information-theoretic approach to quantum theory". Thesis, University of Cambridge, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.614984.
Testo completoKojima, Naoki. "Essays on economic theory in asymmetric information". Toulouse 1, 2001. http://www.theses.fr/2001TOU10093.
Testo completoThis thesis deals with three different subject matters from the aspect of asymmetric information, especially adverse selection: relationship banking in the framework of competition amongst banks ; initial public offering (conflicts of interests between the issuer, the underwriter and investors) ; mechanism of optimal pricing by a monopolistic seller in the presence of budget constraints on the part of buyers and proposition of new approach to this bi-dimensional asymmetric information problem
Smith, Charles Eldon. "An information-processing theory of party identification /". The Ohio State University, 1993. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487848531364663.
Testo completoDunleavy, Andrew J. "Applying information theory to super-cooled liquids". Thesis, University of Bristol, 2014. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.683695.
Testo completoSmith, Julian P. "Neural networks, information theory and knowledge representation". Thesis, University of Edinburgh, 1996. http://hdl.handle.net/1842/20801.
Testo completoBorsten, Leron. "Aspects of M-theory and quantum information". Thesis, Imperial College London, 2010. http://hdl.handle.net/10044/1/6051.
Testo completoKang, Wei. "Correlation and cooperation in network information theory". College Park, Md. : University of Maryland, 2008. http://hdl.handle.net/1903/8355.
Testo completoThesis research directed by: Dept. of Electrical and Computer Engineering. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
Takahashi, Maki. "Studies in relativity and quantum information theory". Thesis, The University of Sydney, 2013. http://hdl.handle.net/2123/9915.
Testo completoSimpson, Mark Aloysius. "Complexity Theory of Leadership and Management Information". ScholarWorks, 2018. https://scholarworks.waldenu.edu/dissertations/6121.
Testo completoZonzo, Giuseppe. "Quantum Information Theory in Condensed Matter Physics". Doctoral thesis, Universita degli studi di Salerno, 2017. http://hdl.handle.net/10556/2625.
Testo completoInthe“standard”Gizburg-Landauapproach,aphasetransitionisintimately connected to a local order parameter, that spontaneously breaks some symmetries. In addition to the “traditional” symmetry-breaking ordered phases, a complex quantum system exhibits exotic phases, without classical counterpart, that can be described, for example, by introducing non-local order parameters that preserve symmetries. In this scenario, this thesis aims to shed light on open problems, such as the localdistinguishabilitybetweengroundstatesofasymmetry-breakingordered phase and the classification of one dimensional quantum orders, in terms of entanglement measures, in systems for which the Gizburg-Landau approach fails. In particular, I briefly introduce the basic tools that allow to understand the nature of entangled states and to quantify non-classical correlations. Therefore, I analyze the conjecture for which the maximally symmetry-breaking ground states (MSBGSs) are the most classical ones, and thus the only ones selected in real-world situations, among all the ground states of a symmetry-breaking ordered phase. I make the conjecture quantitatively precise, by proving that the MSBGSs are the only ones that: i) minimize pairwise quantum correlations, as measured by the quantum discord; ii) are always local convertible, by only applying LOCC transformations; iii) minimize the residual tangle, satisfying at its minimum the monogamy of entanglement. Moreover,Ianalyzehowevolvesthedistinguishability,afterasuddenchange of the Hamiltonian parameters. I introduce a quantitative measure of distinguishability, in terms of the trace distance between two reduced density matrices. Therefore, in the framework of two integrable models that falls in two different classes of symmetries, i.e. XY models in a transverse magnetic field and the N-cluster Ising models, I prove that the maximum of the distinguishability shows a time-exponential decay. Hence, in the limit of diverging time, all the informations about the particular initial ground state disappear, even if a system is integrable. Far away from the Gizburg-Landau scenario, I analyze a family of fullyanalyticalsolvableonedimensionalspin-1/2models,namedtheN-clustermodels in a transverse magnetic field. Regardless of the cluster size N + 2, these modelsexhibitaquantumphasetransition,thatseparatesaparamagneticphase from a cluster one. The cluster phase coresponds to a nematic ordered phase or a symmetry-protected topological ordered one, for even or odd N respectively. Using the Jordan-Wigner transformations, it is possible to diagonalize these models and derive all their spin correlation functions, with which reconstruct their entanglement properties. In particular, I prove that these models have only a non-vanishing bipartite entanglement, as measured by the concurrence, between spins at the endpoints of the cluster, for a magnetic field strong enough. Moreover, I introduce the minimal set of nonlinear ground-states functionals to detect all 1-D quantum orders for systems of spin-1/2 and fermions. I show that the von Neumann entanglement entropy distinguishes a critical systemfromanoncriticalone,becauseofthelogarithmicdivergenceataquantum critical point. The Schmidt gap detect the disorder of a system , because it saturates to a constant value in a paramagnetic phase and goes to zero otherwise. The mutual information, between two subsystems macroscopically separated, identifiesthesymmetry-breakingorderedphases,becauseofitsdependenceon the order parameters. The topological order phases, instead, via their deeply non-locality, can be characterized by analyzing all three functionals. [edited by author]
In aggiunta alle tradizionali fasi ordinate con rottura spontanea di simmetria, ben descritte con un approccio alla Gizburg-Landau, dove una transizione di fase `e intimamente connessa alla rottura spontanea di qualche simmetria e ad un parametro d’ordine locale, un sistema quantistico presenta anche fasi esotiche,senzaanalogoclassico,chesonoperesempiocaratterizzatedaparametri d’ordine non locali, senza una necessaria rottura di simmetria. Partendo da questi presupposti, questa tesi si pone come obiettivo quello di fare luce su alcuni problemi ancora aperti, come la distinguibilit`a tra stati fondamentaliinsistemiquantisticiconrotturaspontaneadisimmetriaelaclassificazionedituttelefasipresentiinsistemiunidimensionalidispin-1/2efermioni, per i quali l’approccio alla Gizburg-Landau non fornisce una descrizione adeguata. Inparticolare,sid`aunaspiegazioneall’ipotesisecondolaqualeglistatifondamentali che rompono massimamente la simmetria sono quelli pi`u classici, e quindi selezionati dalla decoerenza dell’ambiente, tra tutti gli stati fondamentali,edenergeticamenteequivalenti,diunafaseordinataconrotturaspontanea di simmetria. Si dimostra, infatti, che gli stati che rompono massimamente la simmetria sono gli unici stati che soddisfano tre criteri di classicalit`a: i) minimizzano l’entanglement bipartito, come quantificato dalla discord; ii) sono gli uniciversocuituttiglialtristatifondamentalisonolocalmenteconvertibili,mediante LOCC; iii) minimizzano il tangle residuo, soddisfacendo al minimo la monogamia dell’entanglement. Viene analizzato, inoltre, come evolve la distinguibilit`a tra stati fondamentali, dopo un quench dei parametri Hamiltoniani. Dopo aver introdotto una misura quantitativa della distinguibilit`a, in termini della distanza tra due matrici densit`a ridotte, si dimostra, per due sistemi integrabili con diverse classi di simmetria, nel dettaglio il modello XY in campo magnetico e i modelli NclusterIsing,cheladistinguibilit`adecadeesponenzialmenteneltempoequindi, nel limite di tempi lunghi, tutte le informazioni sullo stato fondamentale di partenza si perdono, anche per sistemi integrabili, nei quali la termalizzazione non si verifica. LontanodalloscenarioGizburg-Landau,sianalizzaunafamigliadimodelli di spin-1/2 esattamente risolvibili, nel dettaglio i modelli N-cluster in campo magnetico, che mostrano una transizione tra una fase disordinata e una di tipo cluster, che pu`o essere nematica o topologica, rispettivamente per N pari o dispari. Usando le trasformazioni di Jordan-Wigner `e possibile diagonalizzare questi modelli, ricavare lo stato fondamentale, le funzioni di correlazione fermioniche e tutte le loro propriet`a di entanglement di. Si dimostra che questi modellinonhannoentanglementmultipartito,masoloentanglementbipartito, come misurato dalla concurrence, tra due spin alle estremit`a del cluster, per un campo magnetico sufficientemente intenso. Inoltre, sidimostrachel’entropiadivonNeumann,loSchmidtgapelamutualinformationrappresentanoilsetminimodifunzionalinonlinearidellamatrice densit`a ridotta, mediante le quali caratterizzare tutte le fasi presenti in sistemi unidimensionali di spin -1/2 e fermioni. In particolare, l’entropia di von Neumann caratterizza la criticalit`a del sistema, per la sua divergenza logaritmica al punto critico; lo Schmidt gap caratterizza il disordine di un sistema, perch´e satura ad un valore costante nelle fasi disordinate e va rapidamente a zero altrove; la mutual information cattura le fasi ordinate con rottura spontanea di simmetria, per le quali cio` e `e possibile definire un parametro d’ordine diverso da zero su un supporto finito. Le fasi topologiche, per via della loro natura fortemente non locale, necessitano di tutte e tre i funzionali per essere individuate. [a cura dell'autore]
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