This thesis is the synthesis of theoretical and experimental works performed in the area of quantum foundations, particularly on quantum correlations and experimental tests of multiplicative Bell inequalities. First we begin with a comprehensive theoretical work performed on the foundations of quantum mechanics, focusing on the puzzling concepts of quantum entanglement, and hidden variable theories. Specifically, we present a broad overview of different classes of hidden variable theories such as local, crypto-nonlocal, contextual and non-local theories, along with several Bell like inequalities for these theories, providing theoretical proofs based on quantum mechanics for the falsification of some of these theories. Second we present a body of experimental, and theoretical works performed on a new class of Bell inequalities, i.e., the multiplicative Bell inequalities. We experimentally report the observation of the Bell parameters close to the Tsirelson (quantum) limit, upto a large number of measurement devices $(n)$, and compare the results with a particular deterministic strategy. We also obtain classical bounds for some $n$, and report the experimental violation of these classical limits. We theoretically derive new richer bounds on the CHSH inequality (named after John Clauser, Michael Horne, Abnor Shimony and Richard Holt) and the multiplicative Bell parameter for $n=2$, based on the principle of ``relativistic independence'', and experimentally observe the distribution of Bell parameters as predicted by these bounds.

Non-local forces exist in nature for two reasons. First that the recent experiments on locality are supposed to be accurate enough. Second that there is no local theory that can reproduce all the predictions of orthodox quantum theory which, almost for about a century, have been proved to be correct experimentally again and again. This thesis concerns both of these. A brief discussion of the measurement in quantum theory is followed by two comments which show that the quantum description is frame dependent and that the collapse of the wave-function of a system may occur without the relevant measurement being performed. After this the Bohm model and a modified version of the Bohm model are described. Next we introduce a new method for obtaining the Bell-type inequalities which can be used for testing locality. We derive more inequalities by this method than obtained by other existing procedures. Using Projection Valued(PV) and Positive Operator Valued Measures(POVM) measurements we have designed experiments which violates one of the Bell inequalities by a larger factor than existing violations which in turn could increase the accuracy of experiments to test for non-locality. This is our first result. After discussing the non-locality and non-Lorentz invariant features of the Bohm model, its retarded version, namely Squires' model - which is local and Lorentz invariant - is introduced. A problem with this model, that is the ambiguity in the cases where the wave-function depends on time, is removed by using the multiple-time wave-function. Finally, we apply the model to one of the experiments of locality and prove that it is in good agreement with the orthodox quantum theory.

L'objectif de ce travail de recherche est l'étude des posibilités offertes par une nouvelle approche de l'information quantique basée sur des variables quantiques continues. Lorsque ces variables continues sont portées par le champs éléctromagnétique, un grand nombre de protocoles d'information quantique peuvent être implémentés à l'aide de lasers et d'éléments d'optique linéaire standards. Cette simplicité expérimentale rend cette approche très intéressantes d'un point de vue pratique, en particulier pour le développement des futurs réseaux de communications quantiques. Le travail peut se diviser en deux parties complémentaires. Dans la première partie, plus fondamentale, la relation complexe qui existe entre l'intrication et la nonlocalité de la mécanique quantique est étudiée sur base des variables optiques continues. Ces deux ressources étant essentielles pour l'information quantique, il est nécessaire de bien les comprendre et de bien les caractériser. Dans la seconde partie, orientée vers des applications concrètes, le problème de la correction d'erreur à variables continues est étudié. Pouvoir transmettre et manipuler l'information sans erreurs est nécessaire au bon développemnent de l'information quantique, mais, en pratique, les erreurs sont inévitables. Les codes correcteurs d'erreurs permettent de détecter et corriger ces erreures de manière efficace.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2017-02-13T13:44:40Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) dissertação final.pdf: 3576056 bytes, checksum: 4650485627f1eb13bb131bcbf6ab588a (MD5) / Made available in DSpace on 2017-02-13T13:44:40Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) dissertação final.pdf: 3576056 bytes, checksum: 4650485627f1eb13bb131bcbf6ab588a (MD5) Previous issue date: 2014-03-28 / CAPES / A criação de estados emaranhados em polarização permite testar experimentalmente questões fundamentais da mecânica quântica, tais como os argumentos de EPR sobre a incompletezadateoriaquântica,atravésdadesigualdadeCHSH.Alémdisso,essesestados emaranhados, têm potenciais de aplicações como, por exemplo, em computação quântica e criptografia quântica. Neste trabalho, se estuda uma fonte muito eficiente para a produção de estados de fótons emaranhados em polarização baseada em um interferômetro de tipo Sagnac. Estes fótons correlacionados são criados em um cristal não linear PPKTP mediante o processo de conversão paramétrica descendente (PDC) tipo-II, quando o cristal é bombeado por pulsos de fentossegundos. Verificando as correlações das medidas de polarização produzidas por esta fonte, observamos fortes violações das desigualdades de Bell para estados de polarização, isto é, verificamos a desigualdade CHSH. / Creation of polarization entangled states allows experimentally to test fundamental properties of quantum mechanics, such as the EPR argument about the incompleteness of the quantum theory, through CHSH inequality; in addition to potential applications as in quantum computing and quantum cryptography. This work studies a very efficient sourceofphotonentangledstatesofpolarizationbasedonaSagnacinterferometer. These photons are created from a nonlinear PPKTP crystal pumped by fentosecond pulses by theprocessofparametricdown-conversion(PDC)type-IIpumpedbyfemtosecondpulses. Analysing correlations of polarization measurements produced by this source we observed strong violations of Bell inequalities for the polarization states, i.e, CHSH inequality.

Tsirelson's bound is the upper bound for a Bell inequality which is valid for all quantum mechanical systems. We discuss why Tsirelson's bound was developed by looking at some historical arguments in quantum physics, such as the Einstein-Podolsky-Rosen (EPR) paradox, an argument for the quantum mechanical description of physical reality being incomplete, and local hidden variables. We present the counterargument to those theories, Bell's inequality, which later expanded to include any inequality that a local system fulfills, but that an entangled quantum system can violate. We present the proof of two specific Bell inequalities: the Clauser-Horne-Shimony-Holt (CHSH) inequality and the I3322 inequality. Then the Tsirelson's bound for the CHSH inequality is proven with a simple system of two entangled spin-1/2 particles and with a general argument that is valid for all entangled systems. We give the upper quantum bound for the generalized CHSH inequality, which describes the situation that we have more than two measurement options, by using semidefinite programming. We prove the Tsirelson's bound for the I3322 inequality by using maximally entangled systems and semidefinite programming. Finally, we discuss the upper bounds that are obtained from these different methods. / Tsirelson's gräns är den övre gränsen till en Bell olikhet som är giltig för alla kvantmekaniska system. Vi diskuterar varför Tsirelson's gräns togs fram genom att titta på histroiska argument i kvantfysik, så som Einstein-Podolsky-Rosen (EPR) paradoxen, ett argument som säger att den kvantmekaniska beskrivningen av den fysikaliska verkligheten är offulständig, och lokala gömda variabler. Vi presenterar motargumentet till dessa teorier, Bell's olikheter, som senare generaliserades för att betyda alla olikheter som lokala system uppfyller, men som ett system i kvantsammanflättning kan bryta. Vi presenterar beviset för två specifika Bell olikheter: CHSH olikheten och I3322 olikheten. Sedan bevisas Tsirelson's gräns för CHSH olikheten med ett enkelt system av två sammanflättade spin-1/2 partiklar och ett generellt argument som stämmer för alla sammanflättade system. Vi ger den övre kvant gränsen för den generaliserade Clauser-Horne-Shimony-Holt (CHSH) olikheten, som beskriver situationen då vi har flera valmöjligheter för mätningar, genom att använda semidefinit programmering. Vi bevisar Tsirelson's gräns för I3322 olikheten genom att använda maximalt sammanflättade system och semidefinit programmering. Till slut diskuterar vi de övre gränserna som har erhållits ifrån de olika metoderna.

Device-independent cryptography provides security in various tasks whilst removing an assumption that cryptographers previously thought of as crucial -- complete trust in the machinations of their experimental apparatus. The theory of Bell inequalities as a proof of indeterminism within nature allows for secure device-independent schemes requiring neither trust in the cryptographers' devices nor reliance on the completeness of quantum mechanics. However, the extreme paranoia attributable to the relaxed assumptions within device independence requires an explicit consideration of the previously assumed ability of the experimenters to freely make random choices. This thesis addresses the so-called `free will loophole', presenting Bell tests and associated cryptographic protocols robust against adversarial manipulation of the random number generators with which measurements in a Bell test are selected. We present several quantitative measures for this experimental free will, otherwise known as measurement dependence. We discuss how an eavesdropper maliciously preprogramming the experimenters' untrusted devices can falsely simulate the violation of a Bell inequality. We also bound the amount of Bell violation achievable within a certain degree of measurement dependence. This analysis extends to device-independent randomness expansion, bounding the guessing probability and estimating the amount of privacy amplification required to distil private randomness. The protocol is secure against either arbitrary no-signalling or quantum adversaries. We also consider device-independent key distribution, studying adversarial models that exploit the free will loophole. Finally, we examine a model correlated between the random number generators and Bell devices across multiple runs of a Bell test. This enables an explicit exposition of the optimal cheating strategy and how the correlations manifest themselves within this strategy. We prove that there remain Bell violations for a sufficiently high, yet non-maximal degree of measurement dependence which cannot be simulated by a classical attack, regardless of how many runs of the experiment those choices are correlated over.

Dans une première partie introductive, nous rappelons la description théorique de la propagation de faisceaux optiques en terme des modes solutions de l'équation de propagation dans l'approximation paraxialle. Dans ce cadre, nous présentons les notions de moment cinétique transporté par les faisceaux lumineux, et de sa décomposition en moment cinétique intrinsèque (ou spin) et en moment angulaire.La seconde partie est consacrée au codage de l'information dans les degrés de libertés de polarisation et de modes transverses des faisceaux optiques. Les modes spin-orbites sont définis et un dispositif expérimental optique pour produire ces modes est présenté. Les modes spin-orbites sont alors exploités pour implémenter un protocole de distribution de clés BB84 ne nécessitant pas le partage à priori d'une base de référence.Dans une troisième partie, nous proposons un critère de type inégalité de Bell, qui constitue une condition suffisante pour caractériser la non-séparabilité en spin-orbite d'un faisceau optique classique. Nous montrons ensuite que la notion de modes spin-orbite séparable ou non-séparable constitue une analogie pertinente avec la notion d'intrication d'états quantiques et permet l'étude de certaines de ses propriétés fondamentales. Enfin, une implémentation expérimentale de cette simulation de tests de Bell avec des faisceaux optiques classiques est présentée, ainsi que sa description détaillée dans le cadre de l'optique quantique.Dans une dernière partie, nous nous intéressons à des inégalités de Bell, pour des états quantiques de systèmes quantiques à deux parties, qui sont caractérisées chacune par une variable continue de type angulaire (périodique). Nous montrons comment détecter la non-localité sur ce type de système, avec des inégalités qui sont similaires aux inégalités CHSH; inégalités qui avaient été développées originellement pour des systèmes de type spin 1/2. Nos inégalités, sont construites à partir de la mesure de la corrélation de fonctions angulaires. Nous montrons qu'elles sont en fait la superposition continue d'inégalités CHSH de type spin 1/2. Nous envisageons une possible implémentation expérimentale, où les corrélations mesurées sont les corrélations angulaires du profil transverse des photons intriqués. / We shall present a theoretical description of paraxial beams, showing the propagation modes that arise from the solution of the paraxial equation in free space. We then discuss the angular momentum carried by light beams, with its decomposition in spin and orbital angular momentum and its quantization. We present the polarization and transverse modes of a beam as potential degrees of freedom to encode information. We define the Spin-Orbit modes and explain the experimental methods to produce such modes. We then apply the Spin-Orbit modes to perform a BB84 quantum key distribution protocol without a shared reference frame.We propose a Bell-like inequality criterion as a sufficient condition for the spin-orbit non-separability of a classical laser beam. We show that the notion of separable and non-separable spin-orbit modes in classical optics builds a useful analogy with entangled quantum states, allowing for the study of some of their important mathematical properties. We present a detailed quantum optical description of the experiment in which a comprehensive range of quantum states are considered.Following the study of Bell's inequalities we consider bipartite quantum systems characterized by a continuous angular variable θ. We show how to reveal non-locality on this type of system using inequalities similar to CHSH ones, originally derived for bipartite spin 1/2 like systems. Such inequalities involve correlated measurement of continuous angular functions and are equivalent to the continuous superposition of CHSH inequalities acting on two-dimensional subspaces of the infinite dimensional Hilbert space. As an example, we discuss in detail one application of our results, which consists in measuring orientation correlations on the transverse profile of entangled photons.

We shall present a theoretical description of paraxial beams, showing the propagation modes that arise from the solution of the paraxial equation in free space. We then discuss the angular momentum carried by light beams, with its decomposition in spin and orbital angular momentum and its quantization. We present the polarization and transverse modes of a beam as potential degrees of freedom to encode information. We define the Spin-Orbit modes and explain the experimental methods to produce such modes. We then apply the Spin-Orbit modes to perform a BB84 quantum key distribution protocol without a shared reference frame.We propose a Bell-like inequality criterion as a sufficient condition for the spin-orbit non-separability of a classical laser beam. We show that the notion of separable and non-separable spin-orbit modes in classical optics builds a useful analogy with entangled quantum states, allowing for the study of some of their important mathematical properties. We present a detailed quantum optical description of the experiment in which a comprehensive range of quantum states are considered.Following the study of Bell's inequalities we consider bipartite quantum systems characterized by a continuous angular variable θ. We show how to reveal non-locality on this type of system using inequalities similar to CHSH ones, originally derived for bipartite spin 1/2 like systems. Such inequalities involve correlated measurement of continuous angular functions and are equivalent to the continuous superposition of CHSH inequalities acting on two-dimensional subspaces of the infinite dimensional Hilbert space. As an example, we discuss in detail one application of our results, which consists in measuring orientation correlations on the transverse profile of entangled photons.

L'objectif de ce travail de recherche est l'étude des posibilités offertes par une nouvelle approche de l'information quantique basée sur des variables quantiques continues. Lorsque ces variables continues sont portées par le champs éléctromagnétique, un grand nombre de protocoles d'information quantique peuvent être implémentés à l'aide de lasers et d'éléments d'optique linéaire standards. Cette simplicité expérimentale rend cette approche très intéressantes d'un point de vue pratique, en particulier pour le développement des futurs réseaux de communications quantiques.<p><p>Le travail peut se diviser en deux parties complémentaires. Dans la première partie, plus fondamentale, la relation complexe qui existe entre l'intrication et la nonlocalité de la mécanique quantique est étudiée sur base des variables optiques continues. Ces deux ressources étant essentielles pour l'information quantique, il est nécessaire de bien les comprendre et de bien les caractériser. Dans la seconde partie, orientée vers des applications concrètes, le problème de la correction d'erreur à variables continues est étudié. Pouvoir transmettre et manipuler l'information sans erreurs est nécessaire au bon développemnent de l'information quantique, mais, en pratique, les erreurs sont inévitables. Les codes correcteurs d'erreurs permettent de détecter et corriger ces erreures de manière efficace.<p> / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished