Exact Identification of a Quantum Change Point

TL;DR

This paper develops the optimal quantum measurement strategy to identify the exact point where a quantum source changes its state, providing analytical success probabilities and analyzing both global and local protocols.

Contribution

It introduces the first analytical solution for the optimal quantum change point detection with certainty and success probability calculations.

Findings

Optimal measurement procedure derived for quantum change point detection

Analytical expression for success probability for any sequence length

Oscillatory behavior observed in success probabilities for different change points

Abstract

The detection of change points is a pivotal task in statistical analysis. In the quantum realm, it is a new primitive where one aims at identifying the point where a source that supposedly prepares a sequence of particles in identical quantum states starts preparing a mutated one. We obtain the optimal procedure to identify the change point with certainty---naturally at the price of having a certain probability of getting an inconclusive answer. We obtain the analytical form of the optimal probability of successful identification for any length of the particle sequence. We show that the conditional success probabilities of identifying each possible change point show an unexpected oscillatory behaviour. We also discuss local (online) protocols and compare them with the optimal procedure.