Quantum Relay Channels

2024-11-25

arXiv.org

AI Summary

This work investigates the capacity of the fully quantum relay channel. To address this problem, we propose three novel coding strategies—partial decode-and-forward, measure-and-forward, and auxiliary-assisted forward—and derive three corresponding universal upper bounds on the achievable rates. We establish the first unified capacity analysis framework for fully quantum relay channels, recovering the classical-quantum relay capacity result of Savov et al. (2012) as a special case. Leveraging tools from quantum information theory—including joint typicality, quantum measurement compression, and entanglement-assisted coding—we rigorously prove all bounds. Notably, we fully characterize the exact capacity of Hadamard-type quantum relay channels. The key innovation lies in introducing an entanglement-assisted forwarding mechanism between the relay and the receiver, enabling a systematic characterization of the fundamental limits of quantum information transmission over relay channels.

Technology Category

• Machine Learning: Quantum Machine Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

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.

Problem

• Establish bounds for quantum relay channel communication strategies
• Determine capacity for Hadamard relay channels using partial-decode forward
• Explore entanglement-assisted message transmission in quantum relay channels

Innovation

• Partial decode-forward strategy for quantum relay
• Measure-forward with compressed measurement outcomes
• Assist-forward using entanglement assistance transmission