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

TL;DR

This paper advances the theory of entanglement-assisted classical communication by developing new decoding strategies, proving the existence of a quantum simultaneous decoder for multiple access channels, and analyzing achievable rate regions.

Contribution

It introduces a general packing lemma for entanglement-assisted communication, proves a quantum simultaneous decoder for two-sender channels, and explores rate regions for bosonic multiple access channels.

Findings

Sequential decoding achieves entanglement-assisted capacity.

Existence of a quantum simultaneous decoder for two-sender channels.

Achievable rate region for entanglement-assisted bosonic multiple access channel.

Abstract

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.