Achieving the Han-Kobayashi inner bound for the quantum interference channel by sequential decoding

TL;DR

This paper demonstrates that sequential decoding strategies can achieve the Han-Kobayashi inner bound for quantum interference channels, matching classical bounds and answering an open question in quantum information theory.

Contribution

It introduces a sequential decoding scheme for quantum channels that achieves the Han-Kobayashi inner bound for quantum interference channels, extending classical results to the quantum setting.

Findings

Sequential decoding achieves mutual information rates for cq-channels.

The scheme attains the Chong-Motani-Garg inner bound for ccqq-IC.

It provides a positive answer to an open problem in quantum interference channels.

Abstract

In this paper, we study the power of sequential decoding strategies for several channels with classical input and quantum output. In our sequential decoding strategies, the receiver loops through all candidate messages trying to project the received state onto a `typical' subspace for the candidate message under consideration, stopping if the projection succeeds for a message, which is then declared as the guess of the receiver for the sent message. We show that even such a conceptually simple strategy can be used to achieve rates up to the mutual information for a single sender single receiver channel called cq-channel henceforth, as well as the standard inner bound for a two sender single receiver multiple access channel, called ccq-MAC in this paper. Our decoding scheme for the ccq-MAC uses a new kind of conditionally typical projector which is constructed using a geometric result about how two subspaces interact structurally. As the main application of our methods, we construct an encoding and decoding scheme achieving the Chong-Motani-Garg inner bound for a two sender two receiver interference channel with classical input and quantum output, called ccqq-IC henceforth. This matches the best known inner bound for the interference channel in the classical setting. Achieving the Chong-Motani-Garg inner bound, which is known to be equivalent to the Han-Kobayashi inner bound, answers an open question raised recently by Fawzi et al. (arxiv:1102.2624). Our encoding scheme is the same as that of Chong-Motani-Garg, and our decoding scheme is sequential.