A relay channel is one in which a Source and Destination use an intermediate Relay station in order to improve communication rates. We propose the study of relay channels with classical inputs and quantum outputs and prove that a “partial decode and forward” strategy is achievable. We divide the channel uses into many blocks and build codes in a randomized, block-Markov manner within each block. The Relay performs a standard Holevo-Schumacher-Westmoreland quantum measurement on each block in order to decode part of the Source's message and then forwards this partial message in the next block. The Destination performs a novel “sliding-window” quantum measurement on two adjacent blocks in order to decode the Source's message. This strategy achieves non-trivial rates for classical communication over a quantum relay channel.
A relay channel is one in which a Source and Destination use an intermediate Relay station in order to improve communication rates. We propose the study of relay channels with classical inputs and quantum outputs and prove that a “partial decode and forward” strategy is achievable. We divide the channel uses into many blocks and build codes in a randomized, block-Markov manner within each block. The Relay performs a standard Holevo-Schumacher-Westmoreland quantum measurement on each block in order to decode part of the Source's message and then forwards this partial message in the next block. The Destination performs a novel “sliding-window” quantum measurement on two adjacent blocks in order to decode the Source's message. This strategy achieves non-trivial rates for classical communication over a quantum relay channel.
Communication over a fully quantum relay channel is considered. We establish three bounds based on different coding strategies, i.e., partial decode-forward, measure-forward, and assist-forward. Using the partial decode-forward strategy, the relay decodes part of the information, while the other part is decoded without the relay’s help. The result by Savov et al. (2012) for a classical-quantum relay channel is obtained as a special case. Based on our partial decode-forward bound, the capacity is determined for Hadamard relay channels. In the measure-forward coding scheme, the relay performs a sequence of measurements and then sends a compressed representation of the measurement outcome to the destination receiver. The measure-forward strategy can be viewed as a generalization of the classical compress-forward bound. At last, we consider quantum relay channels with orthogonal receiver components. The assist-forward bound is based on a new approach, whereby the transmitter sends the message to the relay and simultaneously generates entanglement assistance between the relay and the destination receiver. Subsequently, the relay can transmit the message to the destination receiver with rate-limited entanglement assistance.
Communication over a fully quantum relay channel is considered. We establish three bounds based on different coding strategies, i.e., partial decode-forward, measure-forward, and assist-forward. Using the partial-decode forward strategy, the relay decodes part of the information, while the other part is decoded without the relay's help. The result by Savov et al. (2012) for a classical-quantum relay channel is obtained as a special case. Based on our partial-decode forward bound, the capacity is determined for Hadamard relay channels. In the measure-forward coding scheme, the relay performs a sequence of measurements and then sends a compressed representation of the measurement outcome to the destination receiver. The measure-forward strategy can be viewed as a generalization of the classical compress-forward bound. At last, we consider quantum relay channels with orthogonal receiver components. The assist-forward bound is based on a new approach, whereby the transmitter sends the message to the relay and simultaneously generates entanglement assistance between the relay and the destination receiver. Subsequently, the relay can transmit the message to the destination receiver with rate-limited entanglement assistance.
Communication over a fully quantum relay channel is considered. We establish three bounds based on different coding strategies, i.e., partial decode-forward, measure-forward, and assist-forward. Using the partial decode-forward strategy, the relay decodes part of the information, while the other part is decoded without the relay's help. Based on our partial decode-forward bound, the capacity is determined for Hadamard relay channels. In the measure-forward coding scheme, the relay performs a sequence of measurements and then transmits a compressed representation. At last, the assist-forward bound is based on a new approach, whereby the transmitter sends the message to the relay and simultaneously generates entanglement assistance between the relay and the destination receiver. Subsequently, the relay can transmit with rate-limited entanglement assistance.
Optimally encoding classical information in a quantum system is one of the oldest and most fundamental challenges of quantum information theory. Holevo's bound places a hard upper limit on such encodings, while the Holevo-Schumacher-Westmoreland (HSW) theorem addresses the question of how many classical messages can be “packed” into a given quantum system. In this article, we use Sen's recent quantum joint typicality results to prove a one-shot multiparty quantum packing lemma generalizing the HSW theorem. The lemma is designed to be easily applicable in many network communication scenarios. As an illustration, we use it to straightforwardly obtain quantum generalizations of well-known classical coding schemes for the relay channel: multihop, coherent multihop, decode-forward, and partial decode-forward. We provide both finite blocklength and asymptotic results, the latter matching existing classical formulas. Given the key role of the classical packing lemma in network information theory, our packing lemma should help open the field to direct quantum generalization.
Quantum relays are central to both quantum communication and distributed quantum computing, enabling long-distance transmission and modular architectures. Unlike classical repeaters, quantum repeaters preserve coherence without amplifying quantum information, relying on entanglement swapping and quantum error correction to overcome loss and decoherence. In this work, we investigate the transmission of quantum information via quantum relay channels. Our three-terminal relay model captures the trade-off between repeater-assisted and repeaterless communication strategies. Specifically, we propose a partial decode-forward strategy, in which quantum ``message system" consists of two components. The first component is decoded by the relay and then sent to the destination receiver, whereas the second component is decoded by the destination receiver without the relay's help. We analyze both entanglement-assisted and unassisted scenarios. As a special case, the full decode-forward strategy is recovered, with the relay decoding, re-encoding, and forwarding the entire message. Our framework allows for different entanglement topologies between the transmitter, the relay and the destination receiver, recovering known results on entanglement-assisted and unassisted communication. Furthermore, we discuss the interpretation of coding with quantum side information. These findings provide a foundation for designing secure, efficient, and reliable quantum networks and for realizing practical quantum repeaters and long-range quantum key distribution.
Quantum teleportation and Bell measurements are considered in a noisy relay setting. We introduce two quantum relay-channel models with closed-form capacity formulas, motivated by the canonical quantum communication protocols of teleportation and superdense coding. In both models, the sender transmits a qubit, while the relay observes side information about the Pauli errors that occur in the channel and communicates with the receiver through an orthogonal rate-limited link. We develop a compress-forward coding scheme in which the relay compresses the Pauli-error sequence into bins and sends the bin index to the receiver. The receiver uses this partial error information to reduce the effective channel noise before quantum decoding. We show that this strategy is optimal by establishing matching converse bounds for both models.