Asymptotically Optimal Quantum Universal Quickest Change Detection

TL;DR

This paper develops an asymptotically optimal method for quickest change detection in quantum states when the post-change state is unknown, combining quantum measurement strategies with classical algorithms.

Contribution

It introduces a two-stage approach that achieves asymptotic optimality for universal quantum change detection, integrating quantum measurements with classical CUSUM algorithms.

Findings

The proposed method is asymptotically optimal in worst average delay.

Block POVMs preserve quantum relative entropy with arbitrary precision.

A windowed-CUSUM algorithm is adapted for quantum change detection.

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.