Sequential, successive, and simultaneous decoders for entanglement-assisted classical communication

Bennett et al. showed that allowing shared entanglement between a sender and receiver before communication begins dramatically simplifies the theory of quantum channels, and these results suggest that it would be worthwhile to study other scenarios for entanglement-assisted classical communication. In this vein, the present paper makes several contributions to the theory of entanglement-assisted classical communication. First, we rephrase the Giovannetti-Lloyd-Maccone sequential decoding argument as a more general packing lemma and show that it gives an alternate way of achieving the entanglement-assisted classical capacity. Next, we show that a similar sequential decoder can achieve the Hsieh-Devetak-Winter region for entanglement-assisted classical communication over a multiple access channel. Third, we prove the existence of a quantum simultaneous decoder for entanglement-assisted classical communication over a multiple access channel with two senders. This result implies a solution of the quantum simultaneous decoding conjecture for unassisted classical communication over quantum multiple access channels with two senders, but the three-sender case still remains open (Sen recently and independently solved this unassisted two-sender case with a different technique). We then leverage this result to recover the known regions for unassisted and assisted quantum communication over a quantum multiple access channel, though our proof exploits a coherent quantum simultaneous decoder. Finally, we determine an achievable rate region for communication over an entanglement-assisted bosonic multiple access channel and compare it with the Yen-Shapiro outer bound for unassisted communication over the same channel. © 2012 Springer Science+Business Media, LLC

Sequential, successive, and simultaneous decoders for entanglement-assisted classical communication

Bennett et al. showed that allowing shared entanglement between a sender and receiver before communication begins dramatically simplifies the theory of quantum channels, and these results suggest that it would be worthwhile to study other scenarios for entanglement-assisted classical communication. In this vein, the present paper makes several contributions to the theory of entanglement-assisted classical communication. First, we rephrase the Giovannetti-Lloyd-Maccone sequential decoding argument as a more general "packing lemma" and show that it gives an alternate way of achieving the entanglement-assisted classical capacity. Next, we show that a similar sequential decoder can achieve the Hsieh-Devetak-Winter region for entanglement-assisted classical communication over a multiple access channel. Third, we prove the existence of a quantum simultaneous decoder for entanglement-assisted classical communication over a multiple access channel with two senders. This result implies a solution of the quantum simultaneous decoding conjecture for unassisted classical communication over quantum multiple access channels with two senders, but the three-sender case still remains open (Sen recently and independently solved this unassisted two-sender case with a different technique). We then leverage this result to recover the known regions for unassisted and assisted quantum communication over a quantum multiple access channel, though our proof exploits a coherent quantum simultaneous decoder. Finally, we determine an achievable rate region for communication over an entanglement-assisted bosonic multiple access channel and compare it with the Yen-Shapiro outer bound for unassisted communication over the same channel.Comment: 33 pages, 2 figures; v2 contains a proof of the quantum simultaneous decoding conjecture for two-sender quantum multiple access channels; v3 shows how to recover the known unassisted and assisted quantum communication regions with a coherent quantum simultaneous decode

Explicit receivers for pure-interference bosonic multiple access channels

The pure-interference bosonic multiple access channel has two senders and one receiver, such that the senders each communicate with multiple temporal modes of a single spatial mode of light. The channel mixes the input modes from the two users pairwise on a lossless beamsplitter, and the receiver has access to one of the two output ports. In prior work, Yen and Shapiro found the capacity region of this channel if encodings consist of coherent-state preparations. Here, we demonstrate how to achieve the coherent-state Yen-Shapiro region (for a range of parameters) using a sequential decoding strategy, and we show that our strategy outperforms the rate regions achievable using conventional receivers. Our receiver performs binary-outcome quantum measurements for every codeword pair in the senders' codebooks. A crucial component of this scheme is a non-destructive "vacuum-or-not" measurement that projects an n-symbol modulated codeword onto the n-fold vacuum state or its orthogonal complement, such that the post-measurement state is either the n-fold vacuum or has the vacuum removed from the support of the n symbols' joint quantum state. This receiver requires the additional ability to perform multimode optical phase-space displacements which are realizable using a beamsplitter and a laser.Comment: v1: 9 pages, 2 figures, submission to the 2012 International Symposium on Information Theory and its Applications (ISITA 2012), Honolulu, Hawaii, USA; v2: minor change

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

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