Optimal Error Exponents for Composite Sequential Quantum Hypothesis Testing
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910206979473408 |
|---|---|
| author | Simpson, Jacob Paul Palias, Efstratios Jose, Sharu Theresa |
| author_facet | Simpson, Jacob Paul Palias, Efstratios Jose, Sharu Theresa |
| contents | We study the composite sequential quantum hypothesis testing (SQHT) problem, where the objective is to distinguish a null quantum state from a set of alternative quantum states. We propose a mixture-sequential quantum probability ratio test that adaptively selects measurements based on the current mixture estimate of the alternative set, and stops upon the first threshold crossing of the mixture log-likelihood ratio. Under an expected sample size constraint, we show that our proposed strategy simultaneously achieves the Type-I and (worst-case) Type-II error exponents, characterized by the minimal measured relative entropies between the null state and the alternative set. We further establish a matching converse, thereby characterizing the optimal error exponent region. Finally, our results show that achieving vanishing error probabilities in composite SQHT requires an expected sample complexity at least as large as that of sequential testing between two fixed states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04915 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal Error Exponents for Composite Sequential Quantum Hypothesis Testing Simpson, Jacob Paul Palias, Efstratios Jose, Sharu Theresa Quantum Physics Information Theory Statistics Theory We study the composite sequential quantum hypothesis testing (SQHT) problem, where the objective is to distinguish a null quantum state from a set of alternative quantum states. We propose a mixture-sequential quantum probability ratio test that adaptively selects measurements based on the current mixture estimate of the alternative set, and stops upon the first threshold crossing of the mixture log-likelihood ratio. Under an expected sample size constraint, we show that our proposed strategy simultaneously achieves the Type-I and (worst-case) Type-II error exponents, characterized by the minimal measured relative entropies between the null state and the alternative set. We further establish a matching converse, thereby characterizing the optimal error exponent region. Finally, our results show that achieving vanishing error probabilities in composite SQHT requires an expected sample complexity at least as large as that of sequential testing between two fixed states. |
| title | Optimal Error Exponents for Composite Sequential Quantum Hypothesis Testing |
| topic | Quantum Physics Information Theory Statistics Theory |
| url | https://arxiv.org/abs/2605.04915 |