Rate Loss in Quantum Channels with Classical State and Applications for Quantum Broadcast Channels

2026-06-05

AI Summary

This work addresses the rate loss incurred in classical-quantum (CQ) channels due to the absence of channel state information at the receiver. It presents the first rigorous proof that such rate loss is non-negligible in non-commutative CQ channels, with a focus on the three-user non-commutative quantum broadcast channel setting. By integrating information-theoretic analysis, quantum channel modeling, and structured coset code design, the paper proposes a novel coding strategy. Theoretical analysis demonstrates that, compared to conventional independent and identically distributed coding, this coset coding scheme effectively mitigates rate loss and achieves higher communication rates in multi-user non-commutative quantum broadcast channels, thereby highlighting the advantages of structured coding in quantum information transmission.

Abstract

We consider the problem of \textit{rate loss} - a strict penalty suffered in achievable rates due to the lack of channel state information at the receiver (Rx) of a classical-quantum (CQ) channel. First, we identify non-commutative CQ channels and analytically prove a rate loss. Building on this, we next prove that coset-code-based strategies can strictly outperform conventional unstructured IID-code-based strategies for non-commutative 3-user CQ broadcast channels.

Problem

• rate loss
• classical-quantum channel
• channel state information
• quantum broadcast channel
• non-commutative channels

Innovation

• rate loss
• classical-quantum channel
• non-commutative
• coset codes
• quantum broadcast channel