The goal of optimal transport is to map a source probability measure to a destination one with the minimum possible cost. However, the optimal mapping might not be feasible under some practical constraints. One such example is to realize a transport mapping through an information bottleneck. As the optimal mapping may induce infinite mutual information between the source and the destination, the existence of an information bottleneck forces one to resort to some suboptimal mappings. Investigating this type of constrained optimal transport problems is clearly of both theoretical significance and practical interest. In this work, we substantiate a particular form of constrained optimal transport in the context of quantum-to-classical systems by establishing an Output-Constrained Rate-Distortion Theorem similar to the classical case introduced by Yuksel et al. This theorem develops a noiseless communication channel and finds the least required transmission rate R and common randomness Rc to transport a sufficiently large block of n i.i.d. source quantum states, to samples forming a perfectly i.i.d. classical destination distribution, while maintaining the distortion between them. The coding theorem provides operational meanings to the problem of Rate-Limited Optimal Transport, which finds the optimal transportation from source to destination subject to the rate constraints on transmission and common randomness. We further provide an analytical evaluation of the quantum-to-classical rate-limited optimal transportation cost for the case of qubit source state and Bernoulli output distributions with unlimited common randomness. The evaluation results in a transcendental system of equations whose solution provides the rate-distortion curve of the transportation protocol. We further extend this theorem to continuous-variable quantum systems by employing a clipping and quantization argument and using our discrete coding theorem. Moreover, we derive an analytical solution for rate-limited Wasserstein distance of 2nd order for Gaussian quantum systems with Gaussian output distribution. We also provide a Gaussian optimality theorem for the case of unlimited common randomness, showing that Gaussian measurement optimizes the rate in a system with Gaussian source and destination. / Thesis / Doctor of Philosophy (PhD) / We establish a coding theorem for rate-limited quantum-classical optimal transport systems with limited classical common randomness. The coding theorem, referred to as the output-constrained rate-distortion theorem, characterizes the rate region of measurement protocols on a product quantum source state for faithful construction of a given classical destination distribution while maintaining the source-destination distortion below a prescribed threshold with respect to a general distortion observable. This theorem provides a solution to the problem of rate-limited optimal transport, which aims to find the optimal cost of transforming a source quantum state to a destination distribution via a measurement channel with a limited classical communication rate. The coding theorem is further extended to cover Bosonic continuous-variable quantum systems. The analytical evaluation is provided for the case of a qubit measurement system with unlimited common randomness, as well as the case of Gaussian quantum systems.

Optical response of an active medium can substantially be modified when coherent superpositions of states are excited, that is, when systems display quantum coherence and interference. This has led to fascinating applications in atomic and molecular systems. Examples include coherent population trapping, lasing without inversion, electromagnetically induced transparency, cooperative spontaneous emission, and quantum entanglement. We study quantum coherence effects in several quantum optical systems and find interesting applications. We show that quantum coherence can lead to transient Raman lasing and lasing without inversion in short wavelength spectral regions--extreme ultraviolet and x-ray--without the requirement of incoherent pumping. For example, we demonstrate transient Raman lasing at 58.4 nm in Helium atom and transient lasing without inversion at 6.1 nm in Helium-like Boron (triply-ionized Boron). We also investigate dynamical properties of a collective superradiant state prepared by absorption of a single photon when the size of the sample is larger than the radiation wavelength. We show that for large number of atoms such a state, to a good approximation, decays exponentially with a rate proportional to the number of atoms. We also find that the collective frequency shift resulting from repeated emission and reabsorption of short-lived virtual photons is proportional to the number of species in the sample. Furthermore, we examine how a position-dependent excitation phase affects the evolution of entanglement between two dipole-coupled qubits. It turns out that the coherence induced by position-dependent excitation phase slows down the otherwise fast decay of the two-qubit entanglement. We also show that it is possible to entangle two spatially separated and uncoupled qubits via interaction with correlated photons in a cavity quantum electrodynamics setup. Finally, we analyze how quantum coherence can be used to generate continuous-variable entanglement in quantum-beat lasers in steady state and propose possible implementation in quantum lithography.

Submitted by Lucienne Costa (lucienneferreira@ufcg.edu.br) on 2018-05-16T23:56:29Z No. of bitstreams: 1 EDMAR JOSÉ DO NASCIMENTO – TESE (PPGEE) 2017.pdf: 1146136 bytes, checksum: 66fa0c285fd895d4aa000dd5ad1d1eef (MD5) / Made available in DSpace on 2018-05-16T23:56:29Z (GMT). No. of bitstreams: 1 EDMAR JOSÉ DO NASCIMENTO – TESE (PPGEE) 2017.pdf: 1146136 bytes, checksum: 66fa0c285fd895d4aa000dd5ad1d1eef (MD5) Previous issue date: 2018-04-18 / Protocolos para a distribuição quântica de chaves (DQC) permitem que duas partes (Alice e Bob) compartilhem uma chave secreta que pode ser usada para fins criptográficos. A segurança do protocolo é baseada em propriedades da mecânica quântica, ao invés de hipóteses computacionais. Na distribuição quântica de chaves com variáveis contínuas (DQCVC), a informação é codificada nas amplitudes de quadratura do campo eletromagnético quantizado. Quando implementado com variáveis contínuas, o aparato usado na DQC é consideravelmente mais simples que nas implementações convencionais com variáveis discretas, já que se pode utilizar a medição do tipo homódina, ao invés da detecção de fótons. Uma vez realizada a medida, ainda se faz necessária uma etapa de processamento clássico, denominada de reconciliação da informação, a fim de que Alice e Bob possam compartilhar uma cadeia comum de bits. Para que a DQCVC possa ser realizada em distâncias razoáveis (superiores a 30 km), o processo de reconciliação precisa ser feito com eficiências elevadas (superiores a 90%). Entretanto, eficiências dessa ordem para baixas SNRs (signal-to-noise ratio - razão sinal ruído) requerem o uso de códigos clássicos de comprimento bastante elevado e, assim, são difíceis de serem alcançadas. Nesta tese, se propõe o uso dos mapas de Shannon-Kotel’nikov na preparação dos estados quânticos que são usados na DQCVC. Com a utilização desses mapas, é possível aumentar a SNR entre Alice e Bob sem aumentar a variância da modulação de Alice. Dessa forma, o processo de reconciliação se torna mais simples, pois eficiências de reconciliação mais altas são mais facilmente alcançadas em SNRs maiores. Como contribuições desta tese têm-se: a proposição de um protocolo; a definição de um cenário de simulação e a análise do protocolo para dois tipos de mapas (a espiral uniforme de Arquimedes e as curvas geodésicas em um toro planar). / Quantum key distribution (QKD) protocols allow two parties, Alice and Bob, to share a secret key that may be used for cryptographic purposes. The security of QKD is based on quantum mechanics properties instead of computational assumptions. In continuous-variable quantum key distribution (CVQKD), the information is encoded in the quadrature amplitudes of the quantized electromagnetic field. When QKD is implemented with continuous variables, hardware components are much simpler than their discrete variables equivalents. This is mainly due to homodyne detection instead of photon detection. After measuring the transmitted states, it is still necessary to carry out a classical processing stage known as information reconciliation. This stage allows Alice and Bob to share a common sequence of bits. In order to deploy CVQKD over reasonable distances (over 30 km), reconciliation must be done at high efficiencies (over 90%). However, such high efficiencies for low SNRs (signal-to-noise ratio) require long length classical codes and are difficult to be reached. In this thesis, we propose to use Shannon-Kotel’nikov maps for preparing quantum states in CVQKD. By using these maps, it is possible to increase the SNR between Alice and Bob, without increasing Alice’s variance. Thus, reconciliation becomes easier because higher reconciliation efficiencies are more easily reached for higher SNRs. The contributions of this theses are: the proposal of a CVQKD protocol; the statement of a simulation scenario; the analysis of the proposed protocol for two kinds of maps (uniform Archimedes’ spiral and geodesic curves on a flat torus).

This dissertation documents works on two projects, which are broadly related to photonic integration using III-V semiconductor platform for fiber-based optical communication. Our principal project aims to demonstrate continuous variable quantum key distribution (CV-QKD) with InP-based photonic integrated cir cuit at the 1550 nanometer of optical wavelength. CV QKD protocols, in which the key is encoded in the quadrature variables of light, has generated immense interest over the years because of its compatibility with the existing telecom infrastructure. In this thesis, we have proposed a design of a photonic inte grated circuit potentially capable of realizing this protocol with coherent states of light. From the practical perspective, we have basically designed an optical transmitter and an optical receiver capable of carrying out coherent communi cation via the optical fiber. Initially, we established a mathematical model of the transceiver system based on the optical transfer matrix of the foundry spe cific (Fraunhofer Heinrich Hertz Institute-Germany) building blocks. We have shown that our chip design is versatile in the sense that it can support multiple modulation schemes. Based on the mathematical model, we estimated the link budget to assess the feasibility of on-chip implementation of our protocol. Then we ran a circuit level simulation using the process design kit provided by our foundry to put our analysis on a better footing. The encouraging result from this step prompted us to generate the mask layout for our transceiver chips, which we eventually submitted to the foundry. The other project in the thesis grew out of a collaboration with one of our industry partners. The goal of the project is to enhance the performance of a distributed feedback laser emitting at the 1310 nanometer of optical wavelength by optimizing its design. To that end, we first derived the expression for transmission and reflection spectrum for the laser cavity. Those expressions contained parameters which needed to be obtained from the transverse and the longitudinal mode analysis of the laser. We performed the transverse mode analysis and the longitudinal mode analysis with commercially available numerical solvers. Those mode profiles critically depend on the grating physical parameters. Therefore by tweaking grating dimensions one can control the transmission characteristics of the laser.