Conditional contraction coefficients and their applications to quantum networks

2026-08-27

AI Summary

本文引入条件收缩系数以解决量子网络中信息区分度损失的问题，通过结合任意量子参考系统，并开发了包含量子侧信息的统一分析框架。

Abstract

Contraction coefficients quantify the loss of distinguishability induced by a channel and provide a strong form of the data-processing inequality. While standard contraction coefficients ignore auxiliary quantum systems, existing extensions based on complete contraction coefficients require the compared states to have identical reference marginals. In this work, we introduce conditional contraction coefficients, a novel family that incorporates arbitrary quantum reference systems by subtracting the distinguishability already present in the reference system. We develop a general framework for contraction coefficients with such quantum side information, including the corresponding strong-data-processing-inequality (SDPI) constants, expansion coefficients, and relative contraction coefficients. For the trace distance, we show that the optimization can be restricted to orthogonal input states. For the quantum relative entropy, we prove that its conditional contraction coefficient is exactly equal to the contraction coefficient of the conditional mutual information, extending the classical correspondence between relative-entropy contraction and mutual-information contraction to the setting with quantum side information. More generally, we identify structural properties of divergences required for these results and discuss extensions beyond the relative entropy. These results establish a unified framework for analyzing information contraction in quantum network settings, where quantum side information and distributed correlations are intrinsic features of the information-processing task. Applications include an extension of the Polyanskiy-Wu bounds on mutual information contraction, new perspectives on mixing times, and fundamental limits on quantum memories.

Problem

• Conditional contraction coefficients
• quantum networks
• data-processing inequality
• quantum side information
• information contraction

Innovation

• conditional contraction coefficients
• quantum side information
• strong-data-processing-inequality (SDPI) constants
• trace distance
• quantum relative entropy