Exact Identification of a Quantum Change Point
This addresses a fundamental challenge in quantum statistics for researchers in quantum information and change point detection, offering a foundational solution.
The paper tackles the problem of identifying the exact point where a quantum source changes the state of particles, achieving an optimal procedure that guarantees certainty of identification when conclusive, with analytical success probabilities for any sequence length.
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.