An Information-Theoretic Perspective on Quantum Repeaters

Quantum repeaters are a potential solution to current limitations of quantum communication over optical fibers. We consider communication over a quantum broadcast channel with cooperation between the receivers. Through this setting, we provide an information-theoretic perspective on quantum repeaters. First, we observe that entanglement resources alone do not increase the achievable communication rates. By comparison with the recent results by Leditzki et al. (2020), this observation reveals a violation of the BC-MAC duality between the broadcast channel with two receivers and the multiple-access channel with two transmitters. The next form of cooperation addressed is classical conferencing, where Receiver 1 can send classical messages to Receiver 2. We provide a regularized characterization of the classical capacity region and establish a single-letter formula for the special class of Hadamard broadcast channels.

Given both classical conferencing and entanglement resources, Receiver 1 can teleport a quantum state to Receiver 2. This setting is intimately related to quantum repeaters, as the sender, Receiver 1, and Receiver 2 can be viewed as the transmitter, the repeater, and the destination receiver, respectively. When Receiver 1's sole purpose is to help the transmission to Receiver 2, the model reduces to the quantum primitive relay channel. We derive lower and upper bounds for each setting; and conclude with observations on the tradeoff between repeater-aided and repeaterless communication, and the bottleneck flow behavior of quantum repeaters.