Partial decode-forward for quantum relay channels

A relay channel is one in which a Source and Destination use an intermediate Relay station in order to improve communication rates. We propose the study of relay channels with classical inputs and quantum outputs and prove that a "partial decode and forward" strategy is achievable. We divide the channel uses into many blocks and build codes in a randomized, block-Markov manner within each block. The Relay performs a standard Holevo-Schumacher-Westmoreland quantum measurement on each block in order to decode part of the Source's message and then forwards this partial message in the next block. The Destination performs a novel "sliding-window" quantum measurement on two adjacent blocks in order to decode the Source's message. This strategy achieves non-trivial rates for classical communication over a quantum relay channel.Comment: 7 pages, submission to the 2012 International Symposium on Information Theory (ISIT 2012), Boston, MA, US

A Quantum Multiparty Packing Lemma and the Relay Channel

Optimally encoding classical information in a quantum system is one of the oldest and most fundamental challenges of quantum information theory. Holevo's bound places a hard upper limit on such encodings, while the Holevo-Schumacher-Westmoreland (HSW) theorem addresses the question of how many classical messages can be "packed" into a given quantum system. In this article, we use Sen's recent quantum joint typicality results to prove a one-shot multiparty quantum packing lemma generalizing the HSW theorem. The lemma is designed to be easily applicable in many network communication scenarios. As an illustration, we use it to straightforwardly obtain quantum generalizations of well-known classical coding schemes for the relay channel: multihop, coherent multihop, decode-forward, and partial decode-forward. We provide both finite blocklength and asymptotic results, the latter matching existing classical formulas. Given the key role of the classical packing lemma in network information theory, our packing lemma should help open the field to direct quantum generalization.Comment: 20 page

Network information theory for classical-quantum channels

Network information theory is the study of communication problems involving multiple senders, multiple receivers and intermediate relay stations. The purpose of this thesis is to extend the main ideas of classical network information theory to the study of classical-quantum channels. We prove coding theorems for quantum multiple access channels, quantum interference channels, quantum broadcast channels and quantum relay channels. A quantum model for a communication channel describes more accurately the channel's ability to transmit information. By using physically faithful models for the channel outputs and the detection procedure, we obtain better communication rates than would be possible using a classical strategy. In this thesis, we are interested in the transmission of classical information, so we restrict our attention to the study of classical-quantum channels. These are channels with classical inputs and quantum outputs, and so the coding theorems we present will use classical encoding and quantum decoding. We study the asymptotic regime where many copies of the channel are used in parallel, and the uses are assumed to be independent. In this context, we can exploit information-theoretic techniques to calculate the maximum rates for error-free communication for any channel, given the statistics of the noise on that channel. These theoretical bounds can be used as a benchmark to evaluate the rates achieved by practical communication protocols. Most of the results in this thesis consider classical-quantum channels with finite dimensional output systems, which are analogous to classical discrete memoryless channels. In the last chapter, we will show some applications of our results to a practical optical communication scenario, in which the information is encoded in continuous quantum degrees of freedom, which are analogous to classical channels with Gaussian noise.Comment: Ph.D. Thesis, McGill University, School of Computer Science, July 2012, 223 pages, 18 figures, 36 TikZ diagram

Joint source-channel coding for a quantum multiple access channel

Suppose that two senders each obtain one share of the output of a classical, bivariate, correlated information source. They would like to transmit the correlated source to a receiver using a quantum multiple access channel. In prior work, Cover, El Gamal, and Salehi provided a combined source-channel coding strategy for a classical multiple access channel which outperforms the simpler "separation" strategy where separate codebooks are used for the source coding and the channel coding tasks. In the present paper, we prove that a coding strategy similar to the Cover-El Gamal-Salehi strategy and a corresponding quantum simultaneous decoder allow for the reliable transmission of a source over a quantum multiple access channel, as long as a set of information inequalities involving the Holevo quantity hold.Comment: 21 pages, v2: minor changes, accepted into Journal of Physics