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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.

Submitted by Erika Demachki (erikademachki@gmail.com) on 2014-09-05T19:52:53Z No. of bitstreams: 2 Bastos, Wellison Peixoto - 2011.pdf: 686060 bytes, checksum: ca3480442dd033c3262ee9c2c3216240 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2014-09-05T19:52:53Z (GMT). No. of bitstreams: 2 Bastos, Wellison Peixoto - 2011.pdf: 686060 bytes, checksum: ca3480442dd033c3262ee9c2c3216240 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2011-03-04 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Taking advantage of the Faraday rotations that occur in a photonic cristal placed in an optical cavity with low quality factor, we proposed two schemes to obtain the swapping of entanglement of atomic states, useful in quantum communication and quantum computation. They employ three-level atoms in a -configuration, a linearly polarized photon source, a single detector, and a quarter wave plate. Three (four) cavities are used in the first (second) scheme. An additional scheme was also proposed to obtain controlled teleportation of superposition states, partial controlled teleportation of entangled states and controlled teleportation of entanglement. In all schemes we have included the imperfections that affect the system, such as transmission and coupling of photons in optical components, the fraction of photons with a desired polarization, the quantum efficiency of single photon detection, the effective solid angle where the photon are collected, and the rate of emitted photons by the source. Under these realistic conditions we estimate the success probability of each proccess, including the time spent for its realization. / Aproveitando as rotações de Faraday que ocorrem em um cristal fotônico colocado em uma cavidade óptica com baixo fator de qualidade, propusemos dois esquemas para obter a troca de emaranhamento de estados atômicos, útil em comunicação quântica e computação quântica. Eles empregam átomos de três níveis em uma configuração, uma fonte de fótons com polarização linear, um único detector, e uma placa de quarto de onda. Três (quatro) cavidades são usadas no primeiro (segundo) esquema. Um método adicional foi também proposto para obter teletransporte controlado de estados de superposição, teletransporte parcial controlado de estados emaranhados e teletransporte controlado de estados emaranhados. Em todos os esquemas incluímos as imperfeições que afetam o sistema, tais como a transmissão e acoplamento de fótons em componentes ópticos, a fração de fótons com uma polarização desejada, a eficiência quântica da detecção de um único fóton, o ângulo sólido efetivo em que o fótons são coletados e a taxa de fótons emitidos pela fonte. Sob estas condições realistas, estimamos a probabilidade de sucesso de cada processo, incluindo o tempo gasto para sua realização.