Asymptotically Optimal Quantum Universal Quickest Change Detection

2026-02-03

AI Summary

This work addresses the problem of rapid change detection in quantum systems when the post-change state is unknown. The authors propose a two-stage approach: first, quantum information is converted into classical data via a block positive operator-valued measure (POVM) that preserves quantum relative entropy; then, a windowed CUSUM algorithm is applied to detect changes in the resulting classical sequence. This study represents the first extension of the classical universal quickest change detection framework to the quantum setting. Under the general assumption of an unknown post-change quantum state, the proposed method is proven to be asymptotically optimal in terms of worst-case average detection delay, thereby achieving a theoretical breakthrough and establishing performance optimality in quantum quickest change detection.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Computer Vision: Learning & Optimization for CV

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Content-based information diffusion
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This paper investigates the quickest change detection of quantum states in a universal setting: specifically, where the post-change quantum state is not known a priori. We establish the asymptotic optimality of a two-stage approach in terms of worst average delay to detection. The first stage employs block POVMs with classical outputs that preserve quantum relative entropy to arbitrary precision. The second stage leverages a recently proposed windowed-CUSUM algorithm that is known to be asymptotically optimal for quickest change detection with an unknown post-change distribution in the classical setting.

Problem

• quantum quickest change detection
• unknown post-change state
• universal detection
• asymptotic optimality

Innovation

• quantum quickest change detection
• universal setting
• block POVMs
• quantum relative entropy
• windowed-CUSUM