# Quantum Sequential Universal Hypothesis Testing

arXiv: https://arxiv.org/abs/2508.21594 · HTML: https://mlsanity.com/paper/2508.21594/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Aug 2025.

## Built on by (most cited first, 1 of 1)

- [Multi-Armed Sequential Hypothesis Testing by Betting](https://mlsanity.com/paper/2603.17925/) (2026)

## Abstract (arXiv)

Quantum hypothesis testing (QHT) concerns the statistical inference of unknown quantum states. In the general setting of composite hypotheses, the goal of QHT is to determine whether an unknown quantum state belongs to one or another of two classes of states based on the measurement of a number of copies of the state. Prior art on QHT with composite hypotheses focused on a fixed-copy two-step protocol, with state estimation followed by an optimized joint measurement. However, this fixed-copy approach may be inefficient, using the same number of copies irrespective of the inherent difficulty of the testing task. To address these limitations, we introduce the quantum sequential universal test (QSUT), a novel framework for sequential QHT in the general case of composite hypotheses. QSUT builds on universal inference, and it alternates between adaptive local measurements aimed at exploring the hypothesis space and joint measurements optimized for maximal discrimination. QSUT is proven to rigorously control the type I error under minimal assumptions about the hypothesis structure. We present two practical instantiations of QSUT, one based on the Helstrom-Holevo test and one leveraging shallow variational quantum circuits. Empirical results across a range of composite QHT tasks demonstrate that QSUT consistently reduces copy complexity relative to state-of-the-art fixed-copy strategies.