[NCTS TG1.1 Seminar] Conditional contraction coefficients and their applications to quantum networks

• Event Date: 2026-07-21
• Chen, Jhan Yu 陳詹喻
• Quantum Information and Quantum Computing Quantum computing and interdisciplinary applications
• Speaker: Prof. Christoph Hirche (Leibniz University Hannover)  /  Host: Prof. Hao-Chung Cheng
  Place: Rm. 307, 3F, Cosmology Hall, NTU

Title: [NCTS TG1.1 Seminar] Conditional contraction coefficients and their applications to quantum networks
Speaker: Prof. Christoph Hirche (Leibniz University Hannover)
Time: 2026/7/21 (Tue.) 11:00-12:00
Place: Rm. 307, 3F, Cosmology Hall, NTU
 

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 new 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 the 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.