On Finite-Blocklength Noisy Classical-Quantum Channel Coding With Amplitude Damping Errors

2025-09-18

AI Summary

This work addresses the reliability of finite-blocklength classical information transmission over the quantum amplitude damping channel (ADC), demonstrating that uncoded transmission cannot surpass the channel capacity or yield performance gains at any finite blocklength. Method: We propose a joint optimization framework that co-designs classical error-correcting codes and quantum input state preparation within a unified channel coding architecture—termed classical-quantum joint coding. Leveraging finite-blocklength information theory and quantum channel coding theory, we rigorously characterize the achievable rates and block error probability under this scheme. Contribution/Results: The proposed coding strategy significantly enhances transmission reliability, delivering observable quantum performance gains even at moderate-to-short blocklengths. Our analysis identifies a critical pathway to unlocking quantum advantages in non-ideal quantum channels: abandoning the conventional decoupled paradigm of “classical coding + fixed quantum states” in favor of end-to-end joint optimization of classical and quantum encoding resources.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Ad search and search for Web retail

Abstract

We investigate practical finite-blocklength classical-quantum channel coding over the quantum amplitude damping channel (ADC), aiming to transmit classical information reliably through quantum outputs. Our findings indicate that for any finite blocklength, a naive (uncoded) approach fails to offer any advantage over the ADC. Instead, sophisticated encoding strategies that leverage both classical error-correcting codes and quantum input states are crucial for realizing quantum performance gains at finite blocklengths.

Problem

• Finite-blocklength coding for amplitude damping channel
• Transmitting classical information via quantum outputs
• Encoding strategies combining classical and quantum techniques

Innovation

• Combining classical error-correcting codes
• Using sophisticated quantum input states
• Optimizing finite-blocklength channel coding