Arick Grootveld

Arick Grootveld, Haodong Yang, Nandan Sriranga et al.

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.

Arick Grootveld, Biao Chen, Venkata Gandikota

In this work, we revisit the one- and two-sample testing problems: binary hypothesis testing in which one or both distributions are unknown. For the one-sample test, we provide a more streamlined proof of the asymptotic optimality of Hoeffding's likelihood ratio test, which is equivalent to the threshold test of the relative entropy between the empirical distribution and the nominal distribution. The new proof offers an intuitive interpretation and naturally extends to the two-sample test where we show that a similar form of Hoeffding's test, namely a threshold test of the relative entropy between the two empirical distributions is also asymptotically optimal. A strong converse for the two-sample test is also obtained.