Light, which is composed of discrete quanta, or photons, is one of the most fundamental concepts in physics. Being an elementary entity, the behaviour of photons is governed by the rules of quantum mechanics. The ability to create, manipulate and measure quantum states of light is not only useful in foundational tests of quantum theory, but also in a wide range of quantum technologies – which aim to utilize non-classical properties of quantum systems to perform tasks not possible with classical resources. Only recently has it been possible to control the properties of number states of light, which have a fixed photon-number. Two-photon states are central to testing fundamental physical theories (such as locality and reality) and the implementation of quantum information technologies. The versatility of photon-pair states is en- abled by the potential entanglement properties it can posses. Thus controlling the correlations between photons is crucial to both pure and applied physics. To produce a single photon, a photon-pair state can be used. Detection of one photon indicates its twin’s existence. Many applications, such as optical quantum computation, require pure indistinguishable single photons. Heralding single pho- tons from a photon-pair will, in general, produce single photons in a mixed quantum state due to correlations within the pair. A common approach to creating photon-pairs is through the nonlinear sponta- neous four-wave mixing interaction in optical fibres. This thesis presents a theoreti- cal and experimental implementation of a scheme to tailor the spectral correlations within the pairs. Emphasis is placed on engineering the two-photon state such that they are completely uncorrelated. Spatial entanglement is naturally avoided due to the discrete nature of the optical fibre modes. Spectral correlations are eliminated by careful choice of dispersion characteristics and conditions. The purity of the photons generated by this scheme is demonstrated by means of two-photon inter- ference from independent sources. We measure a purity of (85.9 ± 1.6)% with no spectral filtering, exhibiting the usefulness of this source for quantum technologies and applications.

Nanostructures are promising building blocks for quantum technologies due to their reproducible nature and ability to self-assemble into complex structures. However, the need to control these nanostructures represents a key challenge. Hence, this thesis investigates the manipulation and creation of quantum states in certain nanostructures. The results of this thesis can be applied to quantum information processing and to extremely sensitive magnetic-field measurements. In the first research chapter, we propose and examine methods for entangling two (remote) nuclear spins through their mutual coupling to a transient optically excited electron spin. From our calculations we identify the specific molecular properties that permit high entangling power gates for different protocols. In the next research chapter, we investigate another method to create entanglement; this time between two remote electronic spins. This method uses a very sensitive magnetic-field sensor based on a crystal defect that allows the detection of single magnetic moments. The act of sensing the local field constitutes a two-qubit projective measurement. This entangling operation is remarkably robust to imperfections occurring in an experiment. The third research chapter presents an augmented sensor consisting of a nitrogen-vacancy centre for readout and an `amplifier' spin system that directly senses tiny local magnetic fields. Our calculations show that this hybrid structure has the potential to detect magnetic moments with a sensitivity and spatial resolution far beyond that of a sensor based on only a nitrogen-vacancy centre, and indeed this may be the physical limit for sensors of this class. Finally, the last research chapter investigates measurements of magnetic-field strength using an ensemble of spin-active molecules. Here, we describe a quantum strategy that can beat the common standard strategy. We identify the conditions for which this is possible and find that this crucially depends on the decoherence present in the system.

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

Many quantum information protocols rely on the ability to distinguish between entangled quantum states known as Bell states. However, theoretical limits exist on the maximal distinguishability of these entangled states using linear evolution and local measurement (LELM) devices. In the case of two particles entangled in multiple qubit variables, the maximum number of distinguishable Bell states is known. However, in the more general case of two particles entangled in multiple qudit variables, only an upper bound is known under additional assumptions. I have written software in Matlab and Mathematica to explore computationally the maximum number of Bell states that can be distinguished in the case of two particles entangled in a qutrit variable, and the case of two particles entangled in both a qutrit and qubit variable. Using code I have written in Mathematica, I have reduced the number of cases to check for sets of 9 qubit x qutrit Bell states from 94,143,280 to 10,365. Further work needs to be done to computationally check these cases for distinguishability by an LELM apparatus.

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.

Nesta dissertação, descreveremos as primeiras medidas de ruído quântico em um oscilador paramétrico ótico (OPO) bombeado em 780 nm, construído no nosso laboratório. Esse OPO servirá de fonte de estados não clássicos da luz para interação com átomos de rubídio. Faremos uma revisão da teoria clássica do OPO: o bombeamento de um cristal não linear inserido dentro de uma cavidade ótica, produzindo dois feixes intensos de luz (sinal e complementar) com cores distintas. Calcularemos as expressões para o limiar de oscilação, potências de saída dos feixes convertidos e compararemos as principais diferenças entre OPOs com cristais do tipo I e tipo II. Analisaremos a descrição quântica do OPO, calcularemos os espectros de ruído para as quadraturas do bombeio refletido e para as quadraturas dos feixes gêmeos. Veremos que o OPO gera feixes com correlações quânticas, como o emaranhamento tripartido, entres os três feixes envolvidos no processo não linear. O cristal não linear utilizado no nosso experimento é um PPKTP tipo I. Ajustando a temperatura do cristal, podemos gerar feixes próximos da degenerescência até uma diferença de comprimentos de onda de aproximadamente 350 nm. A compressão de ruído quântico observado na diferença das amplitudes dos feixes sinal e complementar é 44%(-2.5 dB). O próximo passo é a implementação da técnica da rotação da elipse de ruído por cavidades óticas, para medir os ruídos de fase dos três campos . Fazendo a verificação do emaranhamento tripartido e determinando a sua dependência com o ruído de fônons inserido pelo cristal, a caracterização do OPO estará completa. A caracterização deste OPO é um passo importante nos objetivos do LMCAL, que é realizar a troca de informação entre luz e átomos em uma rede quântica. / In this dissertation, we will describe the first measurements of quantum noise in an optical parametric oscillator (OPO) pumped at 780 nm, built at our laboratory. This OPO will be the source of nonclassical states of light to interact with rubidium atoms. We will review the classical OPO theory: the pumping of a nonlinear crystal inside a cavity producing two bright light beams (signal and idler) with different colors. We will calculate the power threshold, output power of the converted beams and compare the main differences between type-I and type-II OPO.We will analyze the quantum description of the OPO, and calculate the noise spectrum of the reflected pump quadratures and for the twin beams quadratures. We will observe that the OPO generates beams with quantum correlations, for example, the tripartite entanglement among the three fields involved in the nonlinear phenomena. The nonlinear crystal used in our experiment is a PPKTP type-I. By adjusting the temperature of the crystal, we can generate beams from close to degenerate regime to a difference between them of 350 nm. The squeezing of quantum noise measured in the amplitude quadratures subtraction for signal and idler is 44%(-2.5 dB). The next step is to implement the method of ellipse noise rotation by an optical cavity, to be able to measure phase quadratures of the three different fields. By verifying the tripartite entanglement and determining the phonon noise due to the crystal, our source characterization will be complete. The characterization of this OPO is an important step in LMCAL goals, which is to realize exchange of information between light and atoms in a quantum network.

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.

Realizamos neste trabalho a construção de um Oscilador Paramétrico Ótico triplamente ressonante bombeado por um laser de Titânio Safira sintonizável na faixa entre 730 nm e 800 nm com potencial de extensão. Os feixes emitidos possuem comprimento de onda em torno de 1560 nm que estão na janela de transmissão das fibras óticas, com potência de saída máxima em torno de 420 mW e um limiar de oscilação mínimo de 53(3) mW quando bombeado por 780.126(0.03) nm. Para os feixes gêmeos a finesse da cavidade vale F=155 e as perdas intracavidade 0.05(0.1)%, permitindo, em tese, uma compressão de ruído próxima a 97(6)%. Esse OPO foi construído com o propósito de que o utilizemos como fonte geradora de estados triplamente emaranhados em um sistema de armazenamento e transferência de informação quântica quando em interação com um sistema atômico de rubídio. Medimos a potência de limiar e a eficiência de conversão para cada comprimento de onda do feixe de bombeio utilizado para caracterizar o sistema. / At the present work we conducted the construction of a triply resonant Optical Parametric Oscillator pumped by a Titanium-Sapphire laser, which is tunable between 730 nm to 800 nm. The emitted beams have wavelength around 1560 nm, in the optical fibers transmission window, maximum output of 420 mW and minimum oscillation threshold of 53(3) mW. For the twin beams, the cavity finesse is F=155 mW and the intracavity losses are 0.05(0.10)%, allowing, in principle, a noise compression close to 97(5)%. The present OPO was built having the purpose of being used as source of triply entangled states in a system for quantum information storage and transfer, while interacting with an atomic rubidium system. We measured the power threshold and conversion efficiency for each pump beam wavelength that we used to characterize the system.

Apresentamos nesta tese a primeira geração direta de emaranhamento tripartite entre feixes intensos de luz. Medimos o emaranhamento entre os feixes sinal, complementar e bombeio refletido, produzidos por um Oscilador Paramétrico Ótico (OPO) operando acima do limiar de oscilação. A principal característica do nosso sistema é a diferença entre os comprimentos de onda dos campos (l0 = 532.251 nm, l1 = 1062.102 nm, e l2 = 1066.915 nm). Esta é a primeira medida de emaranhamento entre mais de dois subsistemas produzidos por uma única fonte no âmbito de variáveis contínuas. Para investigar a existência emaranhamento, utilizamos o critério de positividade sob transposição parcial (PPT). Este critério, aplicado a sistemas compostos por estados gaussianos, dispostos em bipartições do tipo 1×(N 1), torna-se necessário e suficiente na demonstração do emaranhamento. Realizamos também a caracterização do emaranhamento produzido quando submetemos os campos a perdas, identificando regiões de parâmetros onde os estados apresentam emaranhamento frágil ou robusto. A fim de garantir que estamos lidando com estados gaussianos, investigamos a estatística das flutuações dos campos, mostrando excelente acordo entre os valores dos momentos de ordem mais alta da fotocorrente medida e os valores esperados para uma distribuição gaussiana. O estudo que apresentamos é um passo importante para a elaboração de uma rede de informação quântica que possibilitará a comunicação entre diferentes sistemas físicos. / We present in this thesis the first direct generation of tripartite entanglement among bright beams of light. We measured the entanglement among signal, idler and reflected pump beams, produced by an Optical Parametric Oscillator (OPO) operating above the threshold. The main feature of our system is the difference between the wavelengths of the fields (l0 = 532.251 nm, l1 = 1062.102 nm, e l2 = 1066.915 nm). This is the first measurement of entanglement among more than two subsystems produced by a single source, in a continuous variable system. In order to investigate the existence of entanglement, we applied the criterion of positivity under partial transposition (PPT). This criterion, applied to systems composed of Gaussian states, arranged in 1×(N1) bipartition, becomes necessary and sufficient to demonstrate entanglement. We also characterized the entanglement when the fields are submitted to losses, identifying regions of parameters where the states have fragile or robust entanglement. To ensure that we are dealing with Gaussian states, we investigate the statistics of the fields, showing excelent agreement among values of higher order moments of the photocurrent measured and expected values for a Gaussian distribution. The present study is an important step in the development of a quantum information network formed by different physical systems.

Investigamos as propriedades quânticas dos feixes de luz produzidos pelo oscilador paramétrico ótico (OPO) acima do limiar, tanto experimental quanto teoricamente. Apresentamos a primeira medida de emaranhamento entre os feixes gêmeos, sinal e complementar. Estes podem possuir frequências óticas muito distintas, correspondentes a centenas de nanometros em comprimento de onda. O emaranhamento entre duas cores possibilita transferir informação quântica entre diferentes regiões do espectro eletromagnético. A demonstração experimental do emaranhamento foi realizada mostrando que a soma de variâncias de observáveis tipo EPR dos campos, a subtração de intensidades e a soma das fases dos feixes, viola uma desigualdade que deve ser necessariamente satisfeita por todos os estados separáveis. Mostramos a presença de squeezing em ambos os observáveis, com os respectivos valores $\\Delta^2 p_- = 0,49(1)$ e $\\Delta^2 q_+ = 0,65(1)$ relativos ao ruído quântico padrão. A desigualdade violada resultou $\\Delta^2 p_- +\\Delta^2 q_+ = 1,14(2)< 2$. Isso solucionou um problema aberto desde 1988, quando se previu teoricamente pela primeira vez a existência desse emaranhamento. Mostramos teoricamente que as correlações quânticas se estendem ao feixe de bombeio refletido pelo OPO, culminando no emaranhamento entre os três feixes envolvidos no processo paramétrico. Tem-se, assim, a geração direta de emaranhamento tripartite entre três regiões muito distintas do espectro. O emaranhamento multicolor amplia ainda mais as possibilidades de conversão da cor da informação quântica, com aplicações em redes quânticas. As diversas melhorias que realizamos em nosso sistema durante a busca pelo emaranhamento bipartite trouxeram uma compreensão mais profunda sobre a física de seu funcionamento, além de tornar nosso OPO uma fonte estável de feixes de luz coerente emaranhados. Este trabalho vem incluir o OPO acima do limiar no ferramental da área de informação quântica com variáveis contínuas. Esperamos em breve aplicações muito interessantes desse sistema. / We investigate the quantum properties of the light beams produced by an optical parametric oscillator (OPO) above threshold, both experimentally and theoretically. We present the first measurement of entanglement between the bright twin beams, signal and idler. These may differ in wavelength by hundreds of nanometers, showing different \'colors\'. This special characteristic allows for the transfer of quantum information between different regions of the electromagnetic spectrum. Entanglement was experimentally demonstrated by showing that the sum of variances of two EPR-like observables, the subtraction of the beams intensities and the sum of their phases, violates an inequality necessarily fulfilled by all separable states. We obtained squeezing in both observables, with the respective values $\\Delta^2 p_- = 0,49(1)$ and $\\Delta^2 q_+ = 0,65(1)$ relative to the shot noise level. The violated inequality resulted $\\Delta^2 p_- + \\Delta^2 q_+ = 1,14(2)< 2$. This solved an old problem, enunciated in 1988, when this effect was theoretically predicted for the first time. We show theoretically that the quantum correlations extend to the pump beam reflected by the OPO as well, culminating in entanglement among the three fields involved in the parametric process. Therefore, the OPO actually produces tripartite entanglement among very distant spectral regions in a direct manner. Multicolor entanglement opens new possibilities in the frequency conversion of quantum information. The improvements we performed in our system in order to achieve this result have brought a deeper understanding of the phenomena involved, as well as a more stable system operation, resulting in the development of a reliable source of bright entangled light beams. This work has finally added the above-threshold OPO to the optical quantum information toolbox. We expect new and exciting applications to come in the near future.