Quantum Proper Scoring Rules: Minimax Estimation and Resource-Theoretic Advantages
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911654521864192 |
|---|---|
| author | AlMasri, M. W. |
| author_facet | AlMasri, M. W. |
| contents | We generalize proper scoring rules to the quantum domain, replacing probability distributions with density operators. We define Quantum Value Functionals via operator convex generators and establish a complete duality theory yielding proper quantum scoring rules. We derive minimax optimal bounds for quantum state tomography under McCarthy-type incentives, proving a Quantum Cramér-Rao-McCarthy Bound that explicitly links minimax risk to the curvature of the generating function and the Quantum Fisher Information. We quantify the economic value of quantum resources (coherence, entanglement, adaptivity) in forecasting tasks, establishing scaling separations between classical and quantum estimation strategies. Our results guide the design of quantum sensors, incentive-compatible quantum data markets, and robust quantum machine learning protocols. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05268 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum Proper Scoring Rules: Minimax Estimation and Resource-Theoretic Advantages AlMasri, M. W. Quantum Physics We generalize proper scoring rules to the quantum domain, replacing probability distributions with density operators. We define Quantum Value Functionals via operator convex generators and establish a complete duality theory yielding proper quantum scoring rules. We derive minimax optimal bounds for quantum state tomography under McCarthy-type incentives, proving a Quantum Cramér-Rao-McCarthy Bound that explicitly links minimax risk to the curvature of the generating function and the Quantum Fisher Information. We quantify the economic value of quantum resources (coherence, entanglement, adaptivity) in forecasting tasks, establishing scaling separations between classical and quantum estimation strategies. Our results guide the design of quantum sensors, incentive-compatible quantum data markets, and robust quantum machine learning protocols. |
| title | Quantum Proper Scoring Rules: Minimax Estimation and Resource-Theoretic Advantages |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.05268 |