A dissertation submitted to the Faculty of Science in partial fulfillment of the requirements for the Degree of Master of Science School of Physics University of Witwatersrand November 1, 2017 / The generation and detection of entangled photons is a topic of interest in quantum communication. With current state-of-the-art methods it is possible to manipulate any degree of freedom (DoF) of photons, e.g, polarisation, transverse momentum, orbital angular momentum and energy. Furthermore, it is possible to combine these DoF to realise hybrid entanglement { entanglement between the DoF of photons. In this dissertation we focus on hybrid entanglement between photon states of coupled orbital angular momentum and polarisation. We engineer hybrid-entanglement using geometric phase control between spatially separated photons produced from spontaneous parametric down conversion. We present a new type of quantum eraser that does not rely on physical path interference. We show that in principle any other degree of freedom can be used and demonstrate this e ectively through polarisation control. The use of high dimensional hybrid photon states in quantum communication, particularly in quantum cryptography, is still in its infancy. Here we tailor photon states that are coupled in their polarisation and spatial DoF (orbital angular momentum) to realise high dimensional encoding alphabets. We show how photons entangled in their internal DoF can be generated and deterministically detected. We exploit them in a demonstration of a high dimensional quantum key distribution protocol and show that our scheme generates secure keys at high rates. / MT 2018

Thesis (M. S.)--Physics, Georgia Institute of Technology, 2009. / Committee Chair: Kuzmich, Alex; Committee Member: Chapman, Michael; Committee Member: Citrin, David; Committee Member: Kennedy, T. A. Brian; Committee Member: Raman, Chandra

Thesis (Ph. D.)--Physics, Georgia Institute of Technology, 2007. / Kennedy, Brian, Committee Member ; Chapman, Michael, Committee Member ; Kuzmich, Alex, Committee Chair ; Raman, Chandra, Committee Member ; Voss, Paul, Committee Member.

Quantum Key Distribution (QKD) is a symmetric key sharing protocol. The theoretical process exploits the principles of quantum physics to underpin a physical security against any form of eavesdropping. QKD not only ensures an information theoretically secure key exchange but also provides an active real-time means of intrusion detection at a physical level. QKD is therefore considered the encryption technology for the next generation of nano-technology powered ICT solutions. The fundamental science at the basis of QKD has been researched and developed into workable solutions with the current focus on the engineering of quantum technology enabled products. The feasibility of integrating QKD systems into conventional communication solutions remains an active field of research. The implementation of QKD across a conventional communication network requires high levels of resources in terms of the network’s reliability, transparency, delay and bandwidth. This limits the maintainable Quality of Service of the network. Investigations towards overcoming these constraints will promote the uptake of QKD as a mainstream technology. There are two classes of technology that focus on the integration of QKD into conventional architecture. The first, and most immediate, development is the adaptation of conventional systems to handle the additional requirements of quantum technology enabled products. In the case of communication networks, all-optical solutions provide the ideal platform for this expansion. This ensures that the quantum data carriers remain in the quantum regime and are manipulated by only the authenticated end users or trusted nodes. The second, quantum technology enabled products, render techniques to manipulate quantum information in an untrusted environment within the network. This involves the development of quantum memories, repeaters and data collision control. The combination of both these classes as a hybrid solution will ensure an optimal Quality of Service for quantum communication networks. The long-term reasearch into quantum networking solutions is presented as the QuantumCity project. The project investigated the long-term stability of a quantum communication network within a live environment. The network is implemented through the adaptation of conventional switched networks. It has provided positive results with various future opportunities available to expand this initiative. The successful operation of the overall solution is of course dependent of the efficiency of the QKD systems themselves. While the European Telecommunication Standards Institute (ETSI) currently drives the standardisation (ETSI ISG-QKD) of QKD, there is a need for the development of supporting technologies. This thesis aims to understand the current gaps in QKD systems and touch on various technologies that will be essential towards the development of a hybrid QKD solution. This will allow the integration of various established QKD technologies in order to optimally utilise conventional communications networks. The technologies focused on include true random number generators, polarisation-encoded QKD in fibre systems and polarisation tracking in free space units. A study and implementation of each technology is presented in this thesis. / Thesis (Ph.D)-University of KwaZulu-Natal, Durban, 2012.

Keywords: entanglement, complexity, entropy, measurement In chapter 1 the basic principles of communication complexity are introduced. Two-party communication is described explicitly, and multi-party communication complexity is described in terms of the two-party communication complexity model. The relation to entropy is described for the classical communication model. Important concepts from quantum mechanics are introduced. More advanced concepts, for example the generalized measurement, are then presented in detail. In chapter 2 the di erent measures of entanglement are described in detail, and concrete examples are provided. Measures for both pure states and mixed states are described in detail. Some results for the Schmidt decomposition are derived for applications in communication complexity. The Schmidt decomposition is fundamental in quantum communication and computation, and thus is presented in considerable detail. Important concepts such as positive maps and entanglement witnesses are discussed with examples. Finally, in chapter 3, the communication complexity model for quantum communication is described. A number of examples are presented to illustrate the advantages of quantum communication in the communication complexity scenario. This includes communication by teleportation, and dense coding using entanglement. A few problems, such as the Deutsch-Jozsa problem, are worked out in detail to illustrate the advantages of quantum communication. The communication complexity of sampling establishes some relationships between communication complexity, the Schmidt rank and entropy. The last topic is coherent communication complexity, which places communication complexity completely in the domain of quantum computation. An important lower bound for the coherent communication complexity in terms of the Schmidt rank is dervived. This result is the quantum analogue to the log rank lower bound in classical communication complexity. / Prof. W.H. Steeb

Leung, Ming Lam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references and index. / Abstracts in English and Chinese. / List of Figures --- p.viii / Chapter 1 --- Overview --- p.1 / Chapter 2 --- Background and Preliminaries --- p.7 / Chapter 2.1 --- Linear Algebra --- p.7 / Chapter 2.2 --- Quantum Mechanics and Quantum Computation --- p.12 / Chapter 2.3 --- Communication Complexity --- p.16 / Chapter 2.4 --- Game Theory and Evolutionary Dynamics --- p.20 / Chapter 2.4.1 --- Multiplayer Strategic Games in Normal-Form --- p.20 / Chapter 2.4.2 --- Classifications of Games --- p.22 / Chapter 2.4.3 --- Mixed Strategies and Correlated Strategies --- p.26 / Chapter 2.4.4 --- Nash Equilibria --- p.28 / Chapter 2.4.5 --- Dynamic Fixed Points and Stability --- p.31 / Chapter 3 --- Classical and Quantum Communication Complexity --- p.35 / Chapter 3.1 --- Summary of Previous Upper Bounds and Lower Bounds --- p.35 / Chapter 3.2 --- Two-way randomized protocol of Symmetric XOR Functions --- p.38 / Chapter 3.3 --- One-way and SMP randomized protocol of Symmetric XOR Functions --- p.41 / Chapter 3.4 --- Significance of Our Results --- p.45 / Chapter 4 --- Quantum Strategic Games and Static Equilibria --- p.49 / Chapter 4.1 --- Brief History of Quantum Game Theory --- p.50 / Chapter 4.2 --- Models of Quantum Strategies --- p.52 / Chapter 4.2.1 --- Meyer's quantum unitary strategies --- p.53 / Chapter 4.2.2 --- EWL-model of quantum strategies --- p.54 / Chapter 4.2.3 --- Zhang's model of quantum strategies --- p.55 / Chapter 4.3 --- Quantum Equilibrium Concepts --- p.58 / Chapter 4.4 --- Relations between Classical and Quantum Equilibria --- p.60 / Chapter 4.5 --- Refinements of Quantum Equilibria --- p.71 / Chapter 4.6 --- Generating Quantum Equilibria and PPAD-completeness --- p.74 / Chapter 5 --- Classical and Quantum Evolutionary Strategy Dynamics --- p.79 / Chapter 5.1 --- Evolutionary Game Theory --- p.80 / Chapter 5.2 --- Dynamic Strategy Evolution --- p.81 / Chapter 5.3 --- Major Properties of Classical Evolutionary Dynamics --- p.83 / Chapter 5.4 --- Analysis of Classical Strategy Evolution in Bimatrix Games --- p.86 / Chapter 5.4.1 --- Division of Regions in Strategy Space --- p.86 / Chapter 5.4.2 --- Symmetric Games --- p.91 / Chapter 5.4.3 --- Zero-Sum Games --- p.100 / Chapter 5.5 --- Quantum Strategy Evolution --- p.101 / Chapter 5.6 --- Significances of Employing Quantum Strategv Evolution --- p.106 / Chapter A Appendix: --- Common Classical Evolutionary Dynamics --- p.113 / Chapter A.1 --- Replicator Dynamics --- p.113 / Chapter A.2 --- Imitation Dynamics --- p.113 / Chapter A.3 --- Best Response Dynamics --- p.116 / Chapter A.4 --- Smoothed Best Response Dynamics --- p.117 / Chapter A.5 --- Differential Dynamics --- p.117 / Chapter A.6 --- Projective Dynamics --- p.121 / Bibliography --- p.123 / Index --- p.132

No description available.

Thesis (Ph.D.) - University of St Andrews, April 2009.

Nesta dissertaÃÃo e proposto um sistema de correÃÃo de erro quÃntico para estados coerentes de luz e um sistema Ãptico completo para a teleportaÃÃo probabilÃstica de qubits codificados na polarizaÃÃo de um fÃton. O trabalho se inicia com a analise de correÃÃo de erro quÃntico com a utilizaÃÃo de redundÃncias. Depois, e apresentada uma forma de correÃÃo de erros utilizando qubits do tipo time-bin e sem acrÃscimo de redundÃncias. Com base nesta abordagem, foi proposto um sistema de correÃÃo de erro quÃntico passivo, isto e, que nao precisa de controle externo de sincronizaÃÃo, para sistemas de comunicaÃÃes quÃnticas que utilizam estados coerentes de luz, utilizando apenas dispositivos opticos lineares. E mostrado, tambÃm, que o sistema de correÃÃo de qubits individuais pode ser usado para corrigirem estados bipartes de qubits. Em seguida, e analisada a teleportaÃÃo de estados quÃnticos e proposto um sistema probabilÃstico de teleportacao de estados quÃnticos de polarizaÃÃo de fÃtons isolados utilizando dispositivos Ãpticos lineares. Por fim, os tÃpicos de correÃÃo de erro e teleportacao sÃo unidos na proposiÃÃo de um sistema probabilÃstico de teleportacao empregando um sistema de correÃÃo de erros na distribuiÃÃo do par de fÃtons entrelaÃados. / In this dissertation it is considered a quantum error correction system for coherent states of light and a complete optical system for probabilistic teleportation of single-photon polarization encoded qubit. Initially, the quantum error correction with the use of redundancy is analyzed. After that, it is presented a form of error correction using time-bin qubit without redundancies. Based on this last approach, a passive quantum error correction system, that is, without external control and synchronization, for quantum communication system employing coherent states, using only linear optical devices, is proposed. It is shown that the quantum error correction system also works for bipartite states of qubits. Following, the teleportation of quantum states is analyzed and an optical system for probabilistic teleportation of single-photon polarization encoded qubit, using only linear optical devices, is proposed. Finally, the error correction and teleportation topics are put together in the proposal of a probabilistic teleportation system using an error correction system for distribution of the entangled pair of photons

For any communication, the conveyed information must be carried by some physical system. If this system is a quantum system rather than a classical one, its behavior will be governed by the laws of quantum mechanics. Hence, the properties of quantum mechanics, such as superpositions and entanglement, are accessible, opening up new possibilities for transferring information. The exploration of these possibilities constitutes the field of quantum communication. The key ingredient in quantum communication is the qubit, a bit that can be in any superposition of 0 and 1, and that is carried by a quantum state. One possible physical realization of these quantum states is to use single photons. Hence, to explore the possibilities of optical quantum communication, photonic quantum states must be generated, transmitted, characterized, and detected with high precision. This thesis begins with the first of these steps: the implementation of single-photon sources generating photonic qubits. The sources are based on photon-pair generation in nonlinear crystals, and designed to be compatible with fiber optical communication systems. To ensure such a compatibility and to create a high-quality source, a theoretical analysis is made, optimizing the coupling of the photons into optical fibers. Based on the theoretical analysis, a heralded single-photon source and a two-crystal source of entangled photons-pairs are experimentally implemented. The source of entangled photons is further developed into a compact source with a narrow bandwidth compatible with standard telecommunication wavelength-division multiplexers, and even further developed to a more stable one-crystal source. The sources are to be used for quantum communication in general and quantum cryptography in particular. Specifically, a heralded single-photon source is implemented and then used for a full test of a decoy-state quantum cryptography protocol. / QC 20100914