Mathematical and Technological Aspects of Quantum Information Processing

Since its genesis, quantum mechanics has proved to be a very accurate model for predicting the behavior of the world below the nanoscale. However, crucial breakthroughs in technology were needed in order to be able to e ectively access and manipulate such small magnitudes. During the last twenty years, the eld of quantum information processing has experienced a growing interest, in its many variants, both theoretically and practically. Despite being still at a very basic stage, expectations are high. The uniqueness of quantum phenomena (superposition of states, creation of entanglement, etc.) have no classical analogue and allow novelties such as another paradigm of computation, more secure com- munications, quantum teleportation, quantum dense coding, etc. which are presented and analyzed here. The aim of this Thesis is to present in a uni ed way the main mathematical methods used in quantum information processing, as well as the state of the art of their corresponding technological implementations. Our contributions are based in making a self-contained presentation; seeking completeness, that is,treating the most relevant elds of research involved, focusing on their relations; and picking the most relevant, insightful references, given the quantity of literature produced in this eld. We also discuss some of the fundamental questions that remain still unanswered, and which are the current lines of research to shed light on them

Cooperative diversity techniques for high-throughput wireless relay networks

Relay communications has attracted a growing interest in wireless communications with application to various enhanced technologies. This thesis considers a number of issues related to data throughput in various wireless relay network models. Particularly, new implementations of network coding (NC) and space-time coding (STC) techniques are investigated to offer various means of achieving high-throughput relay communications. Firstly, this thesis investigates different practical automatic repeat request (ARQ) retransmission protocols based on NC for two-way wireless relay networks to improve throughput efficiency. Two improved NC-based ARQ schemes are designed based on go-back-N and selective-repeat (SR) protocols. Addressing ARQ issues in multisource multidestination relay networks, a new NC-based ARQ protocol is proposed and two packet-combination algorithms are developed for retransmissions at relay and sources to significantly improve the throughput. In relation to the concept of channel quality indicator (CQI) reporting in two-way relay networks, two new efficient CQI reporting schemes are designed based on NC to improve the system throughput by allowing two terminals to simultaneously estimate the CQI of the distant terminal-relay link without incurring additional overhead. The transmission time for CQI feedback at the relays is reduced by half while the increase in complexity and the loss of performance are shown to be negligible. Furthermore, a low-complexity relay selection scheme is suggested to reduce the relay searching complexity. For the acknowledgment (ACK) process, this thesis proposes a new block ACK scheme based on NC to significantly reduce the ACK overheads and therefore produce an enhanced throughput. The proposed scheme is also shown to improve the reliability of block ACK transmission and reduce the number of data retransmissions for a higher system throughput. Additionally, this thesis presents a new cooperative retransmission scheme based on relay cooperation and NC to considerably reduce the number of retransmission packets and im- prove the reliability of retransmissions for a more power efficient and higher throughput system with non-overlapped retransmissions. Moreover, two relay selection schemes are recommended to determine the optimised number of relays for the retransmission. Finally, with respect to cognitive wireless relay networks (CWRNs), this thesis proposes a new cooperative spectrum sensing (CSS) scheme to improve the spectrum sensing performance and design a new CSS scheme based on NC for three-hop CWRNs to improve system throughput. Furthermore, a new distributed space-time-frequency block code (DSTFBC) is designed for a two- hop nonregenerative CWRN over frequency-selective fading channels. The proposed DSTFBC design achieves higher data rate, spatial diversity gain, and decoupling detection of data blocks at all destination nodes with a low-complexity receiver structure