This dissertation consists of three sections. In the first section, we discuss the generation of arbitrary two-qubit entangled states and present three generation methods. The first method is based on the interaction of an atom with classical and quantized cavity fields. The second method is based on the interaction of two coupled two-level atoms with a laser field. In the last method, we use two spin-1/2 systems which interact with a tuned radio frequency pulse. Using those methods we have generated two qubit arbitrary entangled states which is widely used in quantum computing and quantum information. In the second section, we discuss a possible experimental implementation of quantum walk which is based on the passage of an atom through a high-Q cavity. The chirality is determined by the atomic states and the displacement is characterized by the photon number inside the cavity. Our scheme makes quantum walk possible in a cavity QED system and the results could be widely used on quantum computer. In the last section, we investigate the properties of teleporting an arbitrary superposition of entangled Dicke states of any number of atoms (qubits) between two distant cavities. We also studied teleporting continuous variables of an optical field. Teleportation of Dicke states relies on adiabatic passage using multiatom dark states in each cavity and a conditional detection of photons leaking out of both cavities. In the continuous variables teleportation scheme we first reformulate the protocol of quantum teleportation of arbitrary input optical field states in the density matrix form, and established the relation between the P-function of the input and output states. We then present a condition involving squeeze parameter and detection efficiency under which the P-function of the output state becomes the Q function of the input state such that any nonclassical features in the input state will be eliminated in the teleported state. Based on the research in this section we have made it possible of arbitrary atomic Dicke states teleportation from one cavity to another, and this teleortation will play an essential role in quantum communication. Since quantum properties is so important in quantum communication, the condition we give in this section to distinguish classical and quantum teleportation is also important.

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The goal of this thesis is to present evolutionary algorithms, and demonstrate their applicability in quantum computing. As an introduction to evolutionary algorithms, it is applied to the simple but still challenging (from a computational viewpoint) Travelling Salesman Problem (TSP). This example is used to illustrate the e ect of various parameters like selection method, and maximum population size on the accuracy and e ciency of the evolutionary algorithms. For the sample problem, the 48 continental state capitals of the USA, solutions are evolved and compared to the known optimal solution. From this investigation tournament selection was shown to be the most e ective selection method, and that a population of 200 individuals per generation gave the most e ective convergence rates. In the next part of the thesis, evolutionary algorithms are applied to the generation of optimal quantum circuits for the following cases: The identity transformation : Picked for its simplicity as a test of the correct implementation of the evolutionary algorithm. The results of this investigation showed that the solver program functions correctly and that evolutionary algorithms can indeed nd valid solutions for this kind of problem. The work by Ding et al. [16] on optimal circuits for the two-qubit entanglement gate, controlled-S gate as well as the three qubit entanglement gate are solved by means of EA and the results compared. In all cases similar circuits are produced in fewer generations than the application of Ding et al. [16]. The three qubit quantum Fourier transform gate was also attempted, but no convergence was attained. The quantum teleportation algorithm is also investigated. Firstly the nature of the transformation that leads to quantum teleportation is considered. Next an e ective circuit is sought using evolutionary algorithms. The best result is one gate longer than Brassard [11], and seven gates longer than Yabuki [61]. / AFRIKAANSE OPSOMMING: Die doel van hierdie tesis is om evolusionêre algoritmes te ondersoek en hulle toepaslikheid op kwantumkomputasie te demonstreer. As 'n inleiding tot evolusionêre algoritmes is die eenvoudige, maar steeds komputasioneel uitdagende handelsreisigerprobleem ondersoek. Die invloed van die keuse van 'n seleksie metode, sowel as die invloed van die maksimum aantal individue in 'n generasie op die akkuraatheid en e ektiwiteit van die algoritmes is ondersoek. As voorbeeld is die 48 kontinentale hoofstede van die state van die VSA gekies. Die oplossings wat met evolusionêre algoritmes verkry is, is met die bekende beste oplossings vergelyk. Die resultate van hierdie ondersoek was dat toernooi seleksie die mees e ektiewe seleksie metode is, en dat 200 individue per generasie die mees e ektiewe konvergensie tempo lewer. Evolusionêre algoritmes word vervolgens toegepas om optimale oplossings vir die volgende kwantumalgoritmes te genereer: Die identiteitstransformasie: Hierdie geval is gekies as 'n eenvoudige toepassing met 'n bekende oplossing. Die resultaat van hierdie toepassing van die program was dat dit korrek funksioneer, en vinnig by die korrekte oplossings uitkom. Vervolgens is daar ondersoek ingestel na vier van die gevalle wat in Ding et al. [16] bespreek word. Die spesi eke transformasies waarna gekyk is, is 'n optimale stroombaan vir twee kwabis verstrengeling, 'n beheerde-S hek, 'n drie kwabis verstrengelings hek, en 'n drie kwabis kwantum Fourier transform hek. In die eerste drie gevalle stem die oplossings ooreen met die van Ding et al. [16], en is die konvergensie tempo vinniger. Daar is geen oplossing vir die kwantum Fourier transform verkry nie. Laastens is daar na die kwantumteleportasiealgoritme gekyk. Die eerste stap was om te kyk na die transformasie wat in hierdie geval benodig word, en daarna is gepoog om 'n e ektiewe stroombaan te evolueer. Die beste resultaat was een hek langer as Brassard [11], en sewe hekke langer as Yabuki [61].

In this paper the features of quantum systems which lay the foundation of quantum entanglement are studied. General properties of entangled states are discussed, including their entropy and relation to Bell's inequality. Applications of entanglement, namely quantum teleportation and quantum cryptography, are also considered.

A quantum state represents neither properties of a physical system nor anyone s knowledge of its properties. The important question is not what quantum states represent but how they are used as informational bridges. Knowing about some physical situations (its backing conditions), an agent may assign a quantum state to form expectations about other possible physical situations (its advice conditions). Quantum states are objective: only expectations based on correct state assignments are gen- erally reliable. If a quantum state represents anything, it is the objective probabilistic relations between its backing conditions and its advice con- ditions. This paper o¤ers an account of quantum states and their function

Building complex quantum systems has the potential to reveal phenomena that cannot be studied using classical simulation. Photonics has proven to be an effective test-bed for the investigation of such quantum-enhanced technologies, however, the proliferation of bulk optical components is unlikely to be a scalable route towards building more complex devices. Instead, the miniaturisation, inherent phase stability and trivial alignment afforded by integrated photonic systems has been shown to be a promising alternative. In the first half of this thesis, we describe experiments exploiting the quantum interference of three single photons on a reconfigurable integrated photonic chip. We develop a low-loss source of single photons and introduce a low-loss silica-on-silicon waveguide architecture which enables us to show the first genuine quantum interference of three single photons on an integrated platform. A loss-tolerant, element-wise characterisation scheme is developed along with a statistical test to verify that this multi-photon circuit behaves as expected. We then make use of this three-photon interference to detail the first proof-of-principle demonstration of a new intermediate model of quantum computation called boson sampling. Finally, we perform an on-chip demonstration of the quantum teleportation protocol where all key parts --- entanglement preparation, Bell-state analysis and quantum state tomography --- are performed on a reconfigurable photonic chip. The element-wise characterisation scheme developed earlier is shown to be critical to mitigate fabricated component errors. We develop a theoretical model to account for all sources of possible error in the circuit and find good agreement with the measured teleported state fidelities, which exceed the average teleportation fidelity possible with a classical device. We identify the elements of this error budget relevant to scaling and propose improvements to chip characterisation and fabrication in order to achieve high fidelity operation. In the second half, we discuss the use of high efficiency superconducting transition edge sensors in enabling quantum experiments using more photons. We detail the installation and characterisation of these detectors in a new lab in Oxford. We achieve good photon number-resolution and high-efficiency operation. Work to integrate these detectors on the silica-on-silicon waveguide architecture is discussed and we detail the optical and thermal device modelling performed to optimise the on-chip detection efficiency. New, on-chip detectors, fabricated according to this design are shown to operate as expected and achieve high-efficiency and good energy resolution.

Em 1993, Bennett et al. [1] postularam o processo de teletransporte de um estado quântico através do uso de dois canais de comunicação, um canal clássico e outro formado por um par de sistemas emaranhados. Na área de óptica quântica, várias realizações experimentais deste teletransporte foram relatadas [2, 3, 4], tanto no domínio de variáveis contínuas como discretas. Recentemente, foi medido emaranhamento no domínio de variáveis contínuas entre feixes de luz intensos de cores distintas [5, 6, 7]. Utilizando feixes com estas características como canal de comunicação quântico, apresentamos uma proposta para o primeiro teletransporte de informação quântica com troca de informação no domínio de variáveis contínuas entre campos de cores distintas. Resultados experimentais em direção à realização da proposta foram alcançados. Os moduladores eletro-ópticos, necessários na construção e reconstrução dos estados quânticos da luz, foram caracterizados. Quatro cavidades ópticas foram construídas, com requerido pelo protocolo para feixes de luz de cores distintas. Um oscilador paramétrico óptico (OPO) foi construído para a gerar os feixes correlacionados. No entanto, ele apresentou resultados insatisfatórios, atribuídos a um defeito no cristal não linear. Por isso, um OPO com novo cristal e novos espelhos foi projetado e se encontra em fase de construção. Por fim, um tratamento teórico adequado às particularidades da proposta experimental é apresentado. / In 1993, Bennett et al. [1] postulated teleportation of quantum states by means of two communication channels, one classical and the other formed by a pair of entangled systems. In quantum optics, several experimental realizations of this teleportation process have been reported [2, 3, 4], both in the continuous and discrete variables domains. Recently, entanglement in the continuous variables domain between brigth beams of light with different colors were measured [5, 6, 7]. Using beams with these characteristics as a quantum comunication channel, we present a proposal for the first quantum information teleportation with exchange of information in the continuous variables domain between different color fields. Experimental results towards the proposal´s accomplishment have been achieved. The electro-optic modulators, needed in the preparation and reconstruction of quantum states of light, were characterized. Four optical cavities were built, as required by the protocol for multicolored light beams. An optical parametric oscillator (OPO) was built to generate the correlated beams. However, it showed unsatisfactory results, attributed to a defect in the nonlinear crystal. Therefore, an OPO with new crystal and new mirrors was designed and is under construction. Finally, a theoretical treatment appropriate to the particularities of the experimental proposal is presented.

Em 1993, Bennett propôs um protocolo de teletransporte de um estado quântico por meio de dois canais de comunicação de natureza distinta: Um canal clássico, formado por duas vias clássicas de informação, e um canal quântico, formado por um par de sistemas entrelaçados. Após algumas implementações bem-sucedidas no domínio de variáveis discretas, em 1998 surge uma versão de variáveis contínuas do protocolo [1]. No mesmo ano, Furusawa et al. realizam o teletransporte quântico incondicional baseado em variáveis contínuas do campo [2]. Recentemente, o emaranhamento no domínio de variáveis contínuas entre feixes intensos de luz com diferentes cores foi medido [3, 4, 5]. Neste trabalho relatamos os avanços na implementação do protocolo de teletransporte entre campos intensos de cores distintas. Depois de alguns esforços, conseguimos construir um oscilador paramétrico óptico (OPO) que se apresentou como uma fonte razoável de feixes intensos emaranhados. Os equipamentos necessários para a execução do protocolo foram construídos e instalados. Seguiram-se vários testes para garantir o funcionamento combinado de todas as partes. Entre eles, a teleportação de um estado de vácuo não deslocado, onde obtivemos resultados promissores. Após ajustes de configuração e desenvolvimento de técnicas de análise de dados para fornecer a produção, detecção e análise de estados deslocados do campo, o protocolo foi executado com esse tipo de estados. Alcançamos uma fidelidade de 45% para um estado de entrada deslocado, enquanto que a fidelidade considerando apenas as variâncias chegou a 60%. Para comprovar sucesso de nosso protocolo de teletransporte quântico, estão previstas algumas otimizações e alterações na operação do OPO, através das quais esperamos superar em breve a marca de 50% de fidelidade, correspondente ao limite clássico. / In 1993, Bennett et al. [6] proposed a teleportation protocol of a quantum state by means of two communication channels of distinct natures: A classical channel, formed by two classical information pathways, and a quantum channel, formed by a pair of entangled systems. After some successful implementations in the discrete variables domain, in 1998 arises a continuous variables version of the teleportation protocol [1]. In the same year, Furusawa et al. accomplish the unconditional quantum teleportation based on continuous variables of the field. [2]. Recently, entanglement in the continuous variables domain between bright beams of light with different colors was measured [3, 4, 5]. In this work we report the advances on the teleportation protocol implementation between bright fields of distinct colors. After some struggle, we managed to build an Optical Parametric Oscillator (OPO) witch presented it self as a reasonable source of entangled bright beams. The setup required for the execution of the protocol was built and installed. This was followed by several tests to ensure the combined working of all parts. The teleportation of a nondisplaced vacuum state was one of the performed tests, on wich we achieved promising results. After setup adjustments and the developing of data analysis techniques to provide the production, detection and analysis of displaced states of the field, the protocol was run with this kind of states. We reached a fidelity of 45% for a displaced input state, while the fidelity considering only the variances was up to 60%. To prove the success of our quantum teleportation protocol, some optimizations and changes in the operation of the OPO are in plan, whereby we expect soon to surpass the 50% fidelity benchmark, corresponding to the classical limit.

Em 1993, Bennett propôs um protocolo de teletransporte de um estado quântico por meio de dois canais de comunicação de natureza distinta: Um canal clássico, formado por duas vias clássicas de informação, e um canal quântico, formado por um par de sistemas entrelaçados. Após algumas implementações bem-sucedidas no domínio de variáveis discretas, em 1998 surge uma versão de variáveis contínuas do protocolo [1]. No mesmo ano, Furusawa et al. realizam o teletransporte quântico incondicional baseado em variáveis contínuas do campo [2]. Recentemente, o emaranhamento no domínio de variáveis contínuas entre feixes intensos de luz com diferentes cores foi medido [3, 4, 5]. Neste trabalho relatamos os avanços na implementação do protocolo de teletransporte entre campos intensos de cores distintas. Depois de alguns esforços, conseguimos construir um oscilador paramétrico óptico (OPO) que se apresentou como uma fonte razoável de feixes intensos emaranhados. Os equipamentos necessários para a execução do protocolo foram construídos e instalados. Seguiram-se vários testes para garantir o funcionamento combinado de todas as partes. Entre eles, a teleportação de um estado de vácuo não deslocado, onde obtivemos resultados promissores. Após ajustes de configuração e desenvolvimento de técnicas de análise de dados para fornecer a produção, detecção e análise de estados deslocados do campo, o protocolo foi executado com esse tipo de estados. Alcançamos uma fidelidade de 45% para um estado de entrada deslocado, enquanto que a fidelidade considerando apenas as variâncias chegou a 60%. Para comprovar sucesso de nosso protocolo de teletransporte quântico, estão previstas algumas otimizações e alterações na operação do OPO, através das quais esperamos superar em breve a marca de 50% de fidelidade, correspondente ao limite clássico. / In 1993, Bennett et al. [6] proposed a teleportation protocol of a quantum state by means of two communication channels of distinct natures: A classical channel, formed by two classical information pathways, and a quantum channel, formed by a pair of entangled systems. After some successful implementations in the discrete variables domain, in 1998 arises a continuous variables version of the teleportation protocol [1]. In the same year, Furusawa et al. accomplish the unconditional quantum teleportation based on continuous variables of the field. [2]. Recently, entanglement in the continuous variables domain between bright beams of light with different colors was measured [3, 4, 5]. In this work we report the advances on the teleportation protocol implementation between bright fields of distinct colors. After some struggle, we managed to build an Optical Parametric Oscillator (OPO) witch presented it self as a reasonable source of entangled bright beams. The setup required for the execution of the protocol was built and installed. This was followed by several tests to ensure the combined working of all parts. The teleportation of a nondisplaced vacuum state was one of the performed tests, on wich we achieved promising results. After setup adjustments and the developing of data analysis techniques to provide the production, detection and analysis of displaced states of the field, the protocol was run with this kind of states. We reached a fidelity of 45% for a displaced input state, while the fidelity considering only the variances was up to 60%. To prove the success of our quantum teleportation protocol, some optimizations and changes in the operation of the OPO are in plan, whereby we expect soon to surpass the 50% fidelity benchmark, corresponding to the classical limit.

Orientador: Prof. Dr. Fernando Luis da Silva Semião / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2017. / Começaremos esta dissertação introduzindo os conceitos básicos para a compreensão sobre informação quântica. Falaremos sobre qubits, operador densidade e sistemas compostos. Em seguida, discutiremos o uso de emaranhamento como recurso para a realização de protocolos quânticos e apresentaremos métodos para quantificá-lo. Como exemplos da utilidade de emaranhamento em tarefas de comunicação quântica, descreveremos os protocolos de teletransporte e de codificação superdensa. Prosseguiremos discutindo como as características de estados emaranhados levam ao fenômeno da não-localidade e como este fenômeno está relacionado com o protocolo de teletransporte. Em seguida, trataremos da quantização de um modo do campo eletromagnético e mostraremos que o hamiltoniano deste campo é formalmente igual ao de um oscilador harmônico de massa unitária. Discutiremos sobre as propriedades de dois tipos de estados relacionados a este modo do campo, os estados de Fock e os estados coerentes, e comentaremos como estes estados podem ser usados qubits. No último capítulo, apresentaremos o protocolo de teletransporte controlado. Como contribuição, iremos propor um modelo onde usamos qubits codificados em estados de Fock e estados coerentes para realização de tal protocolo. Levaremos em consideração perdas que ocorrem quando estes qubits são guiados através de fibras ópticas no modelo proposto. Introduziremos um parâmetro para quantificar a eficiência deste protocolo e iremos analisar como a performance do teletransporte é afetada pelas perdas na fibra para ambos os tipos de codificação. Para finalizar, estudaremos se existe alguma relação entre não-localidade genuinamente tripartida e a eficiência de teletransporte controlado. / This dissertation starts with an introduction on the basic concepts of quantum information. We then present the concepts of qubits, density operators and composite systems. This is followed by a discussion on how entanglement can be used as a resource for tasks in quantum information. Quantification methods for this resource are also presented. As examples of applications involving entanglement on quantum communication tasks, we describe the quantum teleportation and the superdense coding protocols. We finish this chapter with a discussion on how entanglement is related to the nonlocality phenomenon and how this is related to quantum teleportation. In the following chapter, we study the quantization of a single-mode electromagnetic field, and show that the hamiltonian of this field is formally equivalent to a unit-mass harmonic oscillator.We proceed to discuss the properties of two different types of states associated to the this field namely the Fock and coherent states, and comment on how they can be used to implement photonic qubits. In the last chapter, we present the controlled teleportation protocol. As a contribution, we propose a model where qubits based on either Fock or coherent states are used in that protocol. We take into account losses which occur when these qubits are guided through optical fibers. We introduce a parameter to quantify the efficiency of this protocol and analyze how its performance is affected for both types of encodings. Finally, we study whether or not a correlation between control teleportation efficiency and genuine tripartite nonlocality exists.

Submitted by Bruna Rodrigues (bruna92rodrigues@yahoo.com.br) on 2016-10-10T14:16:22Z No. of bitstreams: 1 TeseRFIG.pdf: 4866078 bytes, checksum: fad89e3fc2a4023db453218c47475574 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-21T13:36:40Z (GMT) No. of bitstreams: 1 TeseRFIG.pdf: 4866078 bytes, checksum: fad89e3fc2a4023db453218c47475574 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-21T13:36:50Z (GMT) No. of bitstreams: 1 TeseRFIG.pdf: 4866078 bytes, checksum: fad89e3fc2a4023db453218c47475574 (MD5) / Made available in DSpace on 2016-10-21T13:36:59Z (GMT). No. of bitstreams: 1 TeseRFIG.pdf: 4866078 bytes, checksum: fad89e3fc2a4023db453218c47475574 (MD5) Previous issue date: 2016-04-01 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / The main focus of this work is to explore the feasibility of conducting the teleportation protocol in scenarios where the presence of an external environment reduces the purity of the input state and the transmission channel. To investigate the behavior of these protocols under realistic conditions, we selected the main decoherence maps reported in the literature concerning the description of this phenomenon, including the representation of mixed states through the Kraus operators and systems in thermal equilibrium whose Hamiltonian is described by the Heisenberg model. In this context, we proved that there are cases in which the in uence of external factors (such as increasing temperature and decoherence rates) and the immersion of those qubits in distinct environments help increasing the similarity between the properties of the original information and the teleported state. In addition, we studied the probabilistic teleportation protocol under the in uence of the same noise conditions analysed for the deterministic protocol, and the results here obtained show that the rst process can outperform the expected value of the average delity of the teleported state. / O foco do presente trabalho consiste em explorar a viabilidade de se realizar o teletransporte de estados quânticos arbitrários em cenários onde a presença de um ambiente externo reduz a pureza do estado de entrada e do canal de transmissão de informação. Para investigar o comportamento destes protocolos em condições realistas, selecionamos os principais mapas de de coerência registrados na literatura relativos à descrição deste fenômeno, incluindo a representação de estados mistos através dos operadores de Kraus e de sistemas em equilíbrio térmico cujo Hamiltoniano é descrito pelo modelo de Heisenberg. Neste contexto, provamos que existem casos nos quais a influência de fatores externos (como o aumento da temperatura e das taxas de de coerência) e a imersão de qubits em ambientes distintos contribui para aumentar a semelhança entre as propriedades da informação original e as do estado teletransportado. Além disso, estudamos o método de teletransporte probabilístico sob a influência dos mesmos tipos de ruídos analisados para o protocolo determinístico, e os resultados aqui apresentados demonstram que o primeiro processo é capaz de aumentar ainda mais o valor esperado da fidelidade média do estado teletransportado.