Classical communication over a quantum interference channel

Abstract

Calculating the capacity of interference channels is a notorious open problem in classical information theory. Such channels have two senders and two receivers, and each sender would like to communicate with a partner receiver. The capacity of such channels is known exactly in the settings of "very strong" and "strong" interference, while the Han-Kobayashi coding strategy gives the best known achievable rate region in the general case. Here, we introduce and study the quantum interference channel, a natural generalization of the interference channel to the setting of quantum information theory. We restrict ourselves for the most part to channels with two classical inputs and two quantum outputs in order to simplify the presentation of our results (though generalizations of our results to channels with quantum inputs are straightforward). We are able to determine the exact classical capacity of this channel in the settings of "very strong" and "strong" interference, by exploiting Winter's successive decoding strategy and a novel two-sender quantum simultaneous decoder, respectively. We provide a proof that a Han-Kobayashi strategy is achievable with Holevo information rates, up to a conjecture regarding the existence of a three-sender quantum simultaneous decoder. This conjecture holds for a special class of quantum multiple access channels with average output states that commute, and we discuss some other variations of the conjecture that hold. Finally, we detail a connection between the quantum interference channel and prior work on the capacity of bipartite unitary gates.

21 pages, 6 figures, v5: Accepted for publication in the IEEE Transactions on Information Theory

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• Polar codes in network quantum information theory
• On simultaneous min-entropy smoothing
• On the near-optimality of one-shot classical communication over quantum channels
• Bounding the forward classical capacity of bipartite quantum channels
• A Quantum Multiparty Packing Lemma and the Relay Channel
• Decoupling by local random unitaries without simultaneous smoothing, and applications to multi-user quantum information tasks
• Optimized protocols for duplex quantum transduction
• Joint source-channel coding for a quantum multiple access channel
• Classical communication cost of a bipartite quantum channel assisted by non-signalling correlations