We experimentally demonstrate an eight-state continuous-variable quantum key distribution (CV-QKD) over atmospheric turbulence channels. The high secret key rate (SKR) is enabled by 4-D multiplexing of 96 channels, i.e., six-channel wavelength-division multiplexing, four-channel orbital angular momentum multiplexing, two-channel polarization multiplexing, and two-channel spatial-position multiplexing. The atmospheric turbulence channel is emulated by a spatial light modulator on which a series of azimuthal phase patterns yielding Andrews' spectrum are recorded. A commercial coherent receiver is implemented at Bob's side, followed by a phase noise cancellation stage, where channel transmittance can be monitored accurately and phase noise can be effectively eliminated. Compared to four-state CV-QKD, eight-state CV-QKD protocol potentially provides a better performance by offering higher SKR, better excess noise tolerance, and longer secure transmission distance. In our proposed CV-QKD system, the minimum transmittances of 0.24 and 0.26 are required for OAM states of 2 (or -2) and 6 (or -6), respectively, to guarantee the secure transmission. A maximum SKR of 3.744 Gb/s is experimentally achievable, while a total SKR of 960 Mb/s can be obtained in case of mean channel transmittances.

We experimentally demonstrate a RF-assisted four-state continuous-variable quantum key distribution (CV-QKD) system in the presence of turbulence. The atmospheric turbulence channel is emulated by two spatial light modulators (SLMs) on which two randomly generated azimuthal phase patterns are recorded yielding Andrews' azimuthal phase spectrum. Frequency and phase locking are not required in our system thanks to the proposed digital phase noise cancellation (PNC) stage. Besides, the transmittance fluctuation can be monitored accurately by the DC level in this PNC stage, which is free of post-processing noise. The mean excess noise is measured to be 0.014, and the maximum secret key rate of >20Mbit/s can be obtained with the transmittance of 0.85, while employing the commercial PIN photodetectors.

Les évolutions récentes de la cryptographie quantique ont permis de proposer sur le marché des appareils de distribution quantique de clé secrète (QKD). Ceci est obtenu en utilisant soit des variables discrètes et des compteurs de photons (DV), soit des variables continues et des systèmes de détection cohérente (CV). Les avancées technologiques s'orientent maintenant vers la réalisation de dispositifs plus petits, moins chers, et plus commodes à utiliser.L'objectif de cette thèse est de mettre en oeuvre un protocole CV-QKD sur un circuit optique intégré en silicium, en utilisant une modulation Gaussienne d'états cohérents. Deux approches sont utilisées: dans la première l'émetteur Alice et le récepteur Bob sont sur le même circuit photonique (chip) pour une validation de principe, et dans la deuxième ils sont séparés.Les valeurs mesurées des paramètres de la communication permettent d'échanger une clé secrète. / During recent years there have been significant developments in quantum cryptography, bringing quantum key distribution (QKD) devices on the market. This can be done by using either discrete variables (DV) and photon counting, or continuous variables (CV) and coherent detection. Current technological evolutions are now aiming at developing smaller, cheaper and more user-friendly devices.This work focuses on the implementation of CV-QKD using silicon photonics techniques, which provide a high degree of integration. This is exploited to build an on-chip realization of a cryptographic protocol, using Gaussian modulation of coherent states. Two different approaches have been used, first by physically implementing the sender (Alice) and the receiver (Bob) on the same chip for validation purposes, and then by having them onto two separate chips. The measured communication parameters give the possibility to extract a secret key

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.

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.