One of the most immediately compelling arguments against the disjunctivist position within the philosophy of perception points to the well-accepted fact that hallucinations can have the same neural cause as veridical perceptions; this is known as the causal argument. Since the main motivation for disjunctivism is to preserve naive realism, critics claim that naive realism is then incompatible with certain, well-accepted claims of neuropsychology, and, thus, disjunctivism is false. After surveying the general arguments for disjunctivism offered by Hinton, Snowden, and Martin, the causal argument is split into a stronger version and a weaker version. The strong argument relies on a narrow conception of the ‘same cause, same effect’ principle and this narrow conception is extremely controversial, ultimately entailing that mental events supervene only on the total brain state of an individual. The weak argument, which embraces a wider conception of the ‘same cause, same effect’ principle finds the disjunctivist position explanatorily redundant. The two major camps within disjunctivism, positive disjunctivism and negative disjunctivism, offer different approaches to the weak argument, and what emerges from the discussion of these two theories is that negative disjunctivism has a major dialectical advantage against positive disjunctivism, and that negative disjunctivism offers a satisfying response to the weak causal argument. M. G. F. Martin offers an insightful analysis of ‘indistinguishability’ and in doing so clarifies the disjunctivist thesis, sets limits to our understanding of our own mental states, and places the burden with the common-kind theorist.

El concepte d'igualtat és fonamental en qualsevol teoria donat que és una noció essencial a l'hora de discernir entre els elements objecte del seu estudi i possibilitar la definició de mecanismes de classificació.Quan totes les propietats són perfectament precises (absència d'incertesa), hom obtè la igualtat clàssica a on dos objectes són considerats iguals si i només si comparteixen el mateix conjunt de propietats. Però, què passa quan considerem l'aparició d'incertesa, com en el cas a on els objectes compleixen una determinada propietat només fins a un cert grau?. Llavors, donat que alguns objectes seran més similars entre si que d'altres, sorgeix la necessitat de una noció gradual del concepte d'igualtat.Aquestes consideracions refermen la idea de que certs contextos requereixen una definició més flexible, que superi la rigidesa de la noció clàssica d'igualtat. Els operadors de T-indistingibilitat semblen bons candidats per aquest nou tipus d'igualtat que cerquem.D'altra banda, La Teoria de l'Evidència de Dempster-Shafer, com a marc pel tractament d'evidències, defineix implícitament una noció d'indistingibilitat entre els elements del domini de discurs basada en la seva compatibilitat relativa amb l'evidència considerada. El capítol segon analitza diferents mètodes per definir l'operador de T-indistingibilitat associat a una evidència donada.En el capítol tercer, després de presentar un exhaustiu estat de l'art en mesures d'incertesa, ens centrem en la qüestió del còmput de l'entropia quan sobre els elements del domini s'ha definit una relació d'indistingibilitat. Llavors, l'entropia hauria de ser mesurada no en funció de l'ocurrència d'events diferents, sinó d'acord amb la variabilitat percebuda per un observador equipat amb la relació d'indistingibilitat considerada. Aquesta interpretació suggereix el "paradigma de l'observador" que ens porta a la introducció del concepte d'entropia observacional.La incertesa és un fenomen present al món real. El desenvolupament de tècniques que en permetin el tractament és doncs, una necessitat. La 'computació amb paraules' ('computing with words') pretén assolir aquest objectiu mitjançant un formalisme basat en etiquetes lingüístiques, en contrast amb els mètodes numèrics tradicionals. L'ús d'aquestes etiquetes millora la comprensibilitat del llenguatge de representació delconeixement, a l'hora que requereix una adaptació de les tècniques inductives tradicionals.En el quart capítol s'introdueix un nou tipus d'arbre de decisió que incorpora les indistingibilitats entre elements del domini a l'hora de calcular la impuresa dels nodes. Hem anomenat arbres de decisió observacionals a aquests nou tipus, donat que es basen en la incorporació de l'entropia observacional en la funció heurística de selecció d'atributs. A més, presentem un algorisme capaç d'induir regles lingüístiques mitjançant un tractament adient de la incertesa present a les etiquetes lingüístiques o a les dades mateixes. La definició de l'algorisme s'acompanya d'una comparació formal amb altres algorismes estàndards. / The concept of equality is a fundamental notion in any theory since it is essential to the ability of discerning the objects to whom it concerns, ability which in turn is a requirement for any classification mechanism that might be defined. When all the properties involved are entirely precise, what we obtain is the classical equality, where two individuals are considered equal if and only if they share the same set of properties. What happens, however, when imprecision arises as in the case of properties which are fulfilled only up to a degree? Then, because certain individuals will be more similar than others, the need for a gradual notion of equality arises.These considerations show that certain contexts that are pervaded with uncertainty require a more flexible concept of equality that goes beyond the rigidity of the classic concept of equality. T-indistinguishability operators seem to be good candidates for this more flexible and general version of the concept of equality that we are searching for.On the other hand, Dempster-Shafer Theory of Evidence, as a framework for representing and managing general evidences, implicitly conveys the notion of indistinguishability between the elements of the domain of discourse based on their relative compatibility with the evidence at hand. In chapter two we are concerned with providing definitions for the T-indistinguishability operator associated to a given body of evidence.In chapter three, after providing a comprehensive summary of the state of the art on measures of uncertainty, we tackle the problem of computing entropy when an indistinguishability relation has been defined over the elements of the domain. Entropy should then be measured not according to the occurrence of different events, but according to the variability perceived by an observer equipped with indistinguishability abilities as defined by the indistinguishability relation considered. This idea naturally leads to the introduction of the concept of observational entropy.Real data is often pervaded with uncertainty so that devising techniques intended to induce knowledge in the presence of uncertainty seems entirely advisable.The paradigm of computing with words follows this line in order to provide a computation formalism based on linguistic labels in contrast to traditional numerical-based methods.The use of linguistic labels enriches the understandability of the representation language, although it also requires adapting the classical inductive learning procedures to cope with such labels.In chapter four, a novel approach to building decision trees is introduced, addressing the case when uncertainty arises as a consequence of considering a more realistic setting in which decision maker's discernment abilities are taken into account when computing node's impurity measures. This novel paradigm results in what have been called --observational decision trees' since the main idea stems from the notion of observational entropy in order to incorporate indistinguishability concerns. In addition, we present an algorithm intended to induce linguistic rules from data by properly managing the uncertainty present either in the set of describing labels or in the data itself. A formal comparison with standard algorithms is also provided.

Un des plus grands challenges dans le domaine de l’information quantique est la génération, manipulation et détection de plusieurs qubits sur des micro-puces. On assiste ainsi à un véritable essor des technologies pour l’information quantique et pour transmettre l’information, les photons ont un grand avantage sur les autres systèmes, grâce à leur grande vitesse et leur immunité contre la décohérence.Mon travail de thèse porte sur la conception, fabrication et caractérisation d’une source de photons intriqués en matériaux semiconducteurs d’une très grande compacité. Ce dispositif fonctionne à température ambiante, et émet dans la bande de longueurs d’onde télécom. Après une présentation des concepts fondamentaux (chap. 1), le chap. 2 explique la conception et la fabrication des dispositifs.Le chap. 3 présente les caractérisations opto-électroniques des échantillons pompés électriquement, et le chap. 4 les résultats des mesures de pertes et des caractérisations non-linéaires optiques (génération de seconde harmonique, conversion paramétrique spontanée et reconstruction de l’intensité spectrale jointe). Les chap. 5 et 6 se concentrent sur la caractérisation des états quantiques générés par un dispositif passif (démonstration de l’indiscernabilité et de l’intrication en énergie-temps) et leur utilisation dans un protocole de distribution de clés quantiques multi-utilisateurs (intrication en polarisation). Finalement le travail sur le premier dispositif produisant des pairs de photons dansles longueurs d’onde télécoms, injecté électriquement et fonctionnant à température ambiante est présenté (chap. 7). / One of the main issues in the domain of quantum information and communication is the generation,manipulation and detection of several qubits on a single chip. Several approaches are currentlyinvestigated for the implementation of qubits on different types of physical supports and a varietyof quantum information technologies are under development: for quantum memories, spectacularadvances have been done on trapped atoms and ions, while to transmit information, photons arethe ideal support thanks to their high speed of propagation and their almost immunity againstdecoherence. My thesis work has been focused on the conception, fabrication and characterization ofa miniaturized semiconductor source of entangled photons, working at room temperature and telecomwavelengths. First the theoretical concepts relevant to understand the work are described (chapter1). Then the conception and fabrication procedures are given (chapter 2). Chapter 3 presents theoptoelectronics characterization of the device under electrical pumping, and chapter 4 the resultson the optical losses measurements and the nonlinear optical characterization (second harmonicgeneration, spontaneous parametric down conversion and joint spectral intensity reconstruction).Chapters 5 and 6 focus on the characterization of the quantum state generated by a passive sample(demonstration of indistinguishability and energy-time entanglement) and its utilization in a multiuserquantum key distribution protocol (polarization entanglement). Finally the work on the firstelectrically driven photon pairs source emitting in the telecom range and working at room temperatureis presented (chapter 7).

O conceito de indistinguibilidade em uma estrutura, entendido como invariância sob os automorfismos dessa estrutura, é apresentado, analisado e aplicado ao exa me do problema filosófico dos objetos indistinguíveis. Especialmente considerada é a versão desse problema que aparece na teoria quântica. / The concept of indistinguishability in a structure, understood as invariance under the automorphisms of that structure, is presented, analysed and applied to the examination of the philosophical problem of indistinguishable objects. Specially considered is the version of this problem that appears in the quantum theory.

I present a series of experimental and theoretical advances in the field of quantum state estimation. Techniques for measuring the quantum state of light that were originally developed for distinguishable photons fail when the particles are indistinguishable. I develop new methods for handling indistinguishability in quantum state estimation. The technique I present provides the first complete description of states of experimentally indistinguishable photons. It allows me to derive the number of parameters needed to describe an arbitrary state and to quantify distinguishability. I demonstrate its use by applying it to the measurement of the quantum polarization state of two and three-photon systems. State characterization is optimal when no redundant information is collected about the state of the system. I present the results of the first optimal characterization of the polarization state of a two-photon system. I show an improved estimation power over the previous state of the art. I also show how the optimal measurements lead to a new description of the quantum state in terms of a discrete Wigner function. It is often desirable to describe the quantum state of a system in terms of properties that are not themselves quantum-mechanical observables. This usually requires a full characterization of the state followed by a calculation of the properties from the parameters characterizing the state. I apply a technique that allows such properties to be determined directly, without a full characterization of the state. This allows one such property, the purity, to be determined in a single measurement, regardless of the size of the system, while the conventional method of determining purity requires a number of measurements that scales exponentially with the system size.

I present a series of experimental and theoretical advances in the field of quantum state estimation. Techniques for measuring the quantum state of light that were originally developed for distinguishable photons fail when the particles are indistinguishable. I develop new methods for handling indistinguishability in quantum state estimation. The technique I present provides the first complete description of states of experimentally indistinguishable photons. It allows me to derive the number of parameters needed to describe an arbitrary state and to quantify distinguishability. I demonstrate its use by applying it to the measurement of the quantum polarization state of two and three-photon systems. State characterization is optimal when no redundant information is collected about the state of the system. I present the results of the first optimal characterization of the polarization state of a two-photon system. I show an improved estimation power over the previous state of the art. I also show how the optimal measurements lead to a new description of the quantum state in terms of a discrete Wigner function. It is often desirable to describe the quantum state of a system in terms of properties that are not themselves quantum-mechanical observables. This usually requires a full characterization of the state followed by a calculation of the properties from the parameters characterizing the state. I apply a technique that allows such properties to be determined directly, without a full characterization of the state. This allows one such property, the purity, to be determined in a single measurement, regardless of the size of the system, while the conventional method of determining purity requires a number of measurements that scales exponentially with the system size.

Le relationnalisme affirme que le caractère phénoménal de la perception est en partie constitué par les objets que l’on voit. Malgré son attrait intuitif, il est souvent rejeté en vertu de l'argument de l'hallucination. L'objectif de cette thèse est de défendre le relationnalisme. L'argument fait valoir que, puisque le relationnalisme ne peut être vrai pour les hallucinations, il doit forcément être faux pour les perceptions aussi. En cela, l'argument repose sur le principe de l’indiscernabilité (IND), affirmant que deux expériences qui sont introspectivement indiscernables les unes des autres ont le même caractère phénoménal. Je considère et rejette les autres versions de l'argument qui ne reposent pas sur l'IND. Bien que largement accepté, aucun support satisfaisant pour l'IND n'a encore été présenté. Dans cette thèse, je soutiens que la défense de l'IND requiert que l’on entende la notion d’indiscernabilité employée dans l'IND en un sens impersonnel. Ensuite, j’identifie ce qui motive l'IND : l'intuition que, en vertu de sa superficialité, la nature d'un caractère phénoménal doit être accessible par l'introspection, de concert avec l’idée qu’il est impossible de nier l'IND sans nier par là même la superficialité des caractères phénoménaux.Je soutiens que le relationnaliste peut nier l'IND tout en préservant la superficialité des caractères phénoménaux en adoptant une thèse négative de l'hallucination et en reconsidérant la nature de la relation entre le caractère phénoménal d’une expérience et l’accès introspectif qu'il peut y avoir. / Relationalism claims that the phenomenal character of perception is constituted by the obtaining of a non-representational psychological relation to mind-independent objects. Although relationalism provides what seems to be the most straight forward and intuitive account of how experience strikes us introspectively, it is very often believed that the argument from hallucination shows that the view is untenable. The aim of this thesis is to defend relationalism against the argument from hallucination. The argument claims that the phenomenal character of hallucination and perception deserves the same account, and that relationalism cannot be true for hallucinations, therefore relationalism must be rejected. This argument relies on the Indistinguishability Principle (IND), the claim that two experiences that are introspectively indistinguishable from each other have the same phenomenal character. Before assessing the plausibility of this principle, I first consider and dismiss versions of the argument which wouldn’t depend on IND.Although widely accepted, no satisfactory support for IND has been presented yet. In this thesis I argue that defending IND requires that we understand the notion of ‘indiscriminability’ employed in IND in an impersonal sense. I then identify what underwrites IND: the intuition that, in virtue of its superficiality, the nature of a phenomenal character must be accessible through introspection, together with the claim that it is not possible to deny IND without denying the superficiality of phenomenal characters too.I argue that the relationalist can deny IND while preserving the superficiality of phenomenal characters. This can be done by adopting a negative view of hallucination and an account of introspection whereby the phenomenal character doesn’t exist independently of one’s introspective awareness of it and where having introspective access to our experience depends on our perceptual access to the world.

Cette thèse porte sur deux types de problèmes de mécanique statistique : il y est question de percolation sur les groupes et de modèles dirigés. Dans le premier cas,il s’agit de réaliser un groupe comme objet géométrique (via la notion de graphe de Cayley), puis de morceler ce dernier aléatoirement. L’étude de ce processus révèle des liens étroits entre les propriétés géométriques d’un groupe et le comportement de la percolation de Bernoulli sur celui-Ci. Dans le second cas, on s’intéresse à des modèles où haut et bas jouent des rôles différents, ce qui permet de rendre un certain nombre de questions accessibles à l’étude rigoureuse.Le chapitre 1 renforce le théorème d’indistinguabilité de Lyons et Schramm en percolation, lequel stipule que les composantes connexes infinies fournies par la percolation de Bernoulli sur un graphe de Cayley ont presque sûrement toutes la même allure. La non-Trivialité de ce renforcement est illustrée par un modèle dirigé qui vérifie la propriété d’indistinguabilité mais pas la propriété renforcée.Le chapitre 2 est le fruit d’un travail réalisé en collaboration avec Vincent Tassion.On y démontre que la valeur du paramètre critique pour la percolation de Bernoulli ne dépend essentiellement que de la structure locale du graphe de Cayley abélien considéré.Dans le chapitre 3, on introduit une version dirigée du modèle DLA, pour laquelle on établit l’existence d’une dynamique en volume infini, un contrôle sur la propagation d’information et des inégalités asymptotiques sur la largeur et la hauteur de l’agrégat. / This thesis deals with two kinds of statistical mechanics problems: percolation ongroups and directed models. In the first case, we realise the group under considerationas a geometric object (via the notion of Cayley graph) before breaking it apartrandomly. The study of this process reveals deep connections between the geometricproperties of a group and the behaviour of Bernoulli percolation on it. In the secondcase, we focus on models where up and down play different roles, which makes severalquestions less hard to tackle.Chapter 1 strengthens the Indistinguishability Theorem of Lyons-Schramm, whichstates that the infinite clusters yielded by a Bernoulli percolation on a Cayley graphalmost surely all look alike. The non-Triviality of this strengthening is illustrated bya directed model that satisfies the Indistinguishability Property but not the StrongIndistinguishability Property.Chapter 2 has been obtained in collaboration with Vincent Tassion. We show thatthe value of the critical parameter for Bernoulli percolation essentially only dependson the local structure of the considered abelian Cayley graph.In Chapter 3, we introduce a directed version of the DLA model, for which weestablish the existence of an infinite volume dynamics, control the propagation ofinformation and prove asymptotic inequalities on the width and height of the cluster.

O conceito de indistinguibilidade em uma estrutura, entendido como invariância sob os automorfismos dessa estrutura, é apresentado, analisado e aplicado ao exa me do problema filosófico dos objetos indistinguíveis. Especialmente considerada é a versão desse problema que aparece na teoria quântica. / The concept of indistinguishability in a structure, understood as invariance under the automorphisms of that structure, is presented, analysed and applied to the examination of the philosophical problem of indistinguishable objects. Specially considered is the version of this problem that appears in the quantum theory.

Analysis and verification of security protocols are typically carried out in two different models of cryptography: formal cryptography and computational cryptography. Formal cryptography, originally inspired by the work of Dolev and Yao [14], takes an abstract and idealized view of security, and develops its proof techniques based on methods and ideas from logic and theory of programming languages. It makes strong assumptions about cryptographic operations by treating them as perfectly-secure symbolic operations. Computational cryptography, on the other hand, has developed its foundations based on complexity theory. Messages are viewed as bit-strings, and cryptographic operations are treated as actual transformations on bit-strings with certain asymptotic properties.In this thesis, we explore the relation between the Dolev-Yao model and the computational model of public-key cryptography in two contexts: indistinguishability and non-malleability of expressions. This problem in the absence of key-cycles is partially addressed in [20, 21] by Herzog. We adapt our approach to use the co-inductive definition of symbolic security, whose private-key treatment was considered in coinduction, and establish our main results as follow: Using a co-inductive approach, we extend the indistinguishability and non-malleability results of Herzog in the presence of key-cycles. By providing a counter-example, we show that the indistinguishability property in this setting is strictly stronger than the non-malleability property, which gives a negative answer to Herzog's conjecture that they are equivalent. we prove that despite the fact that IND-CCA2 security provides non-malleability in our setting, the same result does not hold for IND-CCA1 security. We prove that, under certain hypothesis, our co-inductive formal indistinguishability is computationally-complete in the absence of key-cycles and with respect to any \emph{length-revealing} encryption scheme. In the presence of key-cycles, we prove that the completeness does not hold even with respect to IND-CPA security. / Graduate