Made available in DSpace on 2014-06-12T18:02:37Z (GMT). No. of bitstreams: 2 arquivo2379_1.pdf: 3057093 bytes, checksum: 296f8d7acc9fd1be515e5c4a4e412e9c (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2009 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / Neste trabalho, analisamos a distribuição do emaranhamento sobre redes quânticas usando memórias quânticas para o armazenamento da informação em ensembles atômicos, através de um esquema conhecido como protocolo DLCZ, cujo objetivo é distribuir emaranhamento e efetuar Distribuição Quântica de Chaves sobre grandes distâncias, usando uma arquitetura de repetidores quânticos. Baseado nesta proposta, analisamos, no regime de variáveis discretas, a troca de emaranhamento em cascata entre N pares de ensembles. Nossa análise envolve o mapeamento dos estados na base de número de excitação, e uma restrição ao subespaço onde não mais que uma excitação é armazenada em cada ensemble. Com base nesta última restrição, fizemos análises de tomografia quântica dos campos gerados e as utilizamos para inferir teoricamente o impacto de várias imperfeições sobre os experimentos. Assim, calculamos a concorrência (medida de emaranhamento) do estado resultante depois de várias trocas de emaranhamento, e analisamos sua degradação com o aumento do número de trocas e com o aumento da probabilidade p de geração de uma única excitação nos ensembles atômicos. Também calculamos a violação da desigualdade de Bell CHSH, para estados de polarização dos campos obtidos a partir de pares de estados atômicos delocalizados com a degradação do emaranhamento. Obtemos então um valor máximo de p para os quais ainda podemos violar tal desigualdade após um certo número de trocas, indicando os recursos mínimos totais necessários para efetuar a distribuição quântica de chaves no sistema. Finalmente, através da análise da probabilidade de sucesso na geração de tais estados degradados após um certo tempo, estimamos o tempo de memória necessário para o protocolo suceder após um certo número de trocas de emaranhamento e analisamos como este tempo escala com o comprimento do canal de comunicação

Yes / Various inequalities (Boole inequality, Chung–Erdös inequality, Frechet inequality) for Kolmogorov (classical) probabilities are considered. Quantum counterparts of these inequalities are introduced, which have an extra 'quantum correction' term, and which hold for all quantum states. When certain sufficient conditions are satisfied, the quantum correction term is zero, and the classical version of these inequalities holds for all states. But in general, the classical version of these inequalities is violated by some of the quantum states. For example in bipartite systems, classical Boole inequalities hold for all rank one (factorizable) states, and are violated by some rank two (entangled) states. A logical approach to CHSH inequalities (which are related to the Frechet inequalities), is studied in this context. It is shown that CHSH inequalities hold for all rank one (factorizable) states, and are violated by some rank two (entangled) states. The reduction of the rank of a pure state by a quantum measurement with both orthogonal and coherent projectors, is studied. Bounds for the average rank reduction are given.

It is already known that one can always find a set of measurements on any two-qubit entangled state that will lead to a violation of the CHSH inequality. We provide an explicit state in terms of the angle between Alice's choice of measurements and the angle between Bob's choice of measurements, such that the CHSH inequality is always violated provided Alice's or Bob's choice of inputs are not collinear. We prove that inequalities with a corresponding Bell operator written as a linear combination of tensor products of Pauli matrices, excluding the identity, will generate the most nonlocal correlations using maximally entangled states in our experiment. From this result and a proposition from Horodecki et. al., we are able to construct the state that generates these optimal correlations. To achieve this state in a lab, one party must rotate their qubit using the orthogonal operation we provide and also rotate their Bloch sphere such that all their measurements lie in the same plane. We provide a comprehensive study of how Bell inequalities change when experiments introduce error via imperfect detection efficiency. The original cases of perfect efficiency are covered first and then a more realistic approach, when inefficient detectors are used, will follow. It is shown that less entanglement is needed to demonstrate more nonlocality in some Clasure-Horne-Shimony-Holt (CHSH) experiments when detector inefficiency is introduced. An example of this is shown for any given specific set of measurements in the CHSH Bell experiment. This occurs when one party has a detector of efficiency for each choice of input and the other party makes projective measurements. The efficiency can be pushed down to fifty percent while still violating the CHSH inequality, and for the experimental set-up illustrated, there is more nonlocality with less entanglement. Furthermore, it is shown that if the first party has an imperfect detector for only one choice of inputs rather than two, the efficiency can be brought down arbitrarily close to zero percent while still violating the CHSH inequality. Historically, nonlocality and entanglement were viewed as two equivalent resources, but recently this equality has come under question; these results further support this fundamental difference. Further more, we introduce Mermin's game in the case of relaxed conditions. The original constraints were that when the detectors in separate labs of a two-qubit experiment are in the same setting, then the results should be the same. We require that the outcomes are the same at least part of the time, given by some epsilon variable. Initially, one could find a maximum violation of one-fourth by allowing to parties to share the singlet state and have measurement settings one-hundred and twenty degrees apart from one another. By allowing some epsilon error in the perfect correlations regime, one can find a maximum violation of minus one plus the square root of two using the singlet state and measurement inputs that achieve Tsirelson's bound for the CHSH experiment. The reason is that we show Mermin's inequality is technically the CHSH inequality "in disguise", but with using constraints the CHSH experiment does not use. We derive Mermin's inequality under new conditions and give the projective measurements needed to violate maximally.

In this paper, we introduce the motivation for Bell inequalities and give some background on two different types: CHSH and Mermin's inequalities. We present a proof for each and then show that certain quantum states can violate both of these inequalities. We introduce a new result stating that for four given measurement directions of spin, two respectively from Alice and two from Bob, which are able to produce a violation of the Bell inequality for an arbitrary shared quantum state will also violate the Bell inequality for a maximally entangled state. Then we provide another new result that characterizes all of the two-qubit states that violate Mermin's 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.

Dans cette thèse,nous étudions comment exploiter des contraintes spatio-temporelles,notamment le principe d'impossibilité de transmission supraluminique,dans le but de créer des primitives cryptographiques sûres,par exemple la vérification de position ou la "mise en gage de bit''(bit commitment). D'après le principe d'impossibilité de transmission supraluminique,aucun vecteur physique d'information ne peut voyager plus vite que la vitesse de la lumière. Ce principe entraîne une contrainte sur le temps de communication entre deux points éloignés. Ce délai dans le transfert d'information peut être utilisé comme une contrainte temporelle interdisant la communication. En cryptographie multi-agents,il est connu que l'hypothèse de non-communication entre les agents permet de réaliser de manière sécurisée de nombreuses primitives comme la "mise en gage de bit'' et l'un des buts de cette thèse est de comprendre à quel point les contraintes spatio-temporelles peuvent être exploitèes pour simuler des scénarios de non-communication. Dans la première partie de cette thèse nous étudions comment utiliser une contrainte de non-communication pour essayer de vérifier la position d'une personne.Dans la dernière partie,nous nous penchons sur deux exemples de protocoles de ``mise en gage de bit'' relativistes afin d'en étudier la sécurité contre des adversaires classiques. Pour conclure cette thèse,nous mentionnons quelques problèmes ouverts intéréssants. Ces problèmes ouverts peuvent être très utiles pour comprendre le rôle de contraintes spatio-temporelles,par exemple de l'impossibilité de transmission supraluminique,dans la conception de primitives cryptographiques parfaitement sûres. / In this thesis we have studied how to exploit relativistic constraints such as the non-superluminal signalling principle to design secure cryptographic primitives like position-verification and bit commitment. According to non-superluminal signalling principle, no physical carrier of information can travel faster than the speed of light. This put a constraint on the communication time between two distant stations. One can consider this delay in information transfer as a temporal non-communication constraint. Cryptographic primitives like bit-commitment, oblivious transfer can be implemented with perfect secrecy under such non-communication assumption between the agents. The first part of this thesis has studied how non-signalling constraints can be used for secure position verification. Here, we have discussed about a strategy which can attack any position verification scheme. In the next part of this thesis we have discussed about the nonlocal games, relevant for studying relativistic bit commitment protocols. We have established an upper bound on the classical value of such family of games. The last part of this thesis discusses about two relativistic bit commitment protocols and their security against classical adversaries. We conclude this thesis by giving a brief summary of the content of each chapter and mentioning interesting open problems. These open problems can be very useful for better understanding of the role of spacetime constraints such as non-superluminal signalling in designing perfectly secure cryptographic primitives.