Distributed Compression and Squashed Entanglement

A single quantum state can be shared by many distant parties. In this thesis, we try to characterize the information contents of such distributed states by defining the multiparty information and the multiparty squashed entanglement, two steps toward a general theory of multiparty quantum information. As a further step in that direction, we partially solve the multiparty distributed compression problem where multiple parties use quantum communication to faithfully transfer their shares of a state to a common receiver. We build a protocol for multiparty distributed compression based on the fully quantum Slepian-Wolf protocol and prove both inner and outer bounds on the achievable rate region. We relate our findings to previous results in information theory and discuss some possible applications.Comment: M.Sc thesis submitted to the Physics department of McGill University, 107 pages, 14 figure

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

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

Classical codes for quantum broadcast channels

We discuss two techniques for transmitting classical information over quantum broadcast channels. The first technique is a quantum generalization of the superposition coding scheme for the classical broadcast channel. We use a quantum simultaneous nonunique decoder and obtain a simpler proof of the rate region recently published by Yard et al. in independent work. Our second result is a quantum Marton coding scheme, which gives the best known achievable rate region for quantum broadcast channels. Both results exploit recent advances in quantum simultaneous decoding developed in the context of quantum interference channels. © 2012 IEEE

Classical codes for quantum broadcast channels

We present two approaches for transmitting classical information over quantum broadcast channels. The first technique is a quantum generalization of the superposition coding scheme for the classical broadcast channel. We use a quantum simultaneous nonunique decoder and obtain a proof of the rate region stated in [Yard et al., IEEE Trans. Inf. Theory 57 (10), 2011]. Our second result is a quantum generalization of the Marton coding scheme. The error analysis for the quantum Marton region makes use of ideas in our earlier work and an idea recently presented by Radhakrishnan et al. in arXiv:1410.3248. Both results exploit recent advances in quantum simultaneous decoding developed in the context of quantum interference channels.Comment: v4: 20 pages, final version to appear in IEEE Transactions on Information Theor

The free space optical interference channel

Semiclassical models for multiple-user optical communication cannot assess the ultimate limits on reliable communication as permitted by the laws of physics. In all optical communications settings that have been analyzed within a quantum framework so far, the gaps between the quantum limit to the capacity and the Shannon limit for structured receivers become most significant in the low photon-number regime. Here, we present a quantum treatment of a multiple-transmitter multiple-receiver multi-spatial-mode free-space interference channel with diffraction-limited loss and a thermal background. We consider the performance of a laser-light (coherent state) encoding in conjunction with various detection strategies such as homodyne, heterodyne, and joint detection. Joint detection outperforms both homodyne and heterodyne detection whenever the channel exhibits very strong interference. We determine the capacity region for homodyne or heterodyne detection when the channel has strong interference, and we conjecture the existence of a joint detection strategy that outperforms the former two strategies in this case. Finally, we determine the Han-Kobayashi achievable rate regions for both homodyne and heterodyne detection and compare them to a region achievable by a conjectured joint detection strategy. In these latter cases, we determine achievable rate regions if the receivers employ a recently discovered minentropy quantum simultaneous decoder. © 2011 IEEE