Quantum change point

TL;DR

This paper explores quantum change point detection, providing analytical solutions for optimal detection and demonstrating that joint measurements outperform local strategies in identifying sudden changes in quantum states.

Contribution

It introduces an analytical expression for the maximum detection probability and compares joint versus local measurement strategies in quantum change point detection.

Findings

Joint measurements significantly outperform local strategies.

Optimal detection probability can be analytically derived for large sequences.

Global quantum measurements better detect local changes in quantum states.

Abstract

Sudden changes are ubiquitous in nature. Identifying them is of crucial importance for a number of applications in medicine, biology, geophysics, and social sciences. Here we investigate the problem in the quantum domain, considering a source that emits particles in a default state, until a point where it switches to another state. Given a sequence of particles emitted by the source, the problem is to find out where the change occurred. For large sequences, we obtain an analytical expression for the maximum probability of correctly identifying the change point when joint measurements on the whole sequence are allowed. We also construct strategies that measure the particles individually and provide an online answer as soon as a new particle is emitted by the source. We show that these strategies substantially underperform the optimal strategy, indicating that quantum sudden changes, although happening locally, are better detected globally.