Stability of Maximum-Entropy Inference in Finite Dimensions
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909867224072192 |
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| author | Tian, James |
| author_facet | Tian, James |
| contents | We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints. Given expectation values of finitely many observables, the feasible set of states is convex but typically non-unique. The maximum-entropy principle selects the Gibbs state that agrees with the data while remaining maximally unbiased. We prove that convergence of moments and entropy implies convergence of states in trace norm, derive explicit quantitative bounds linking data and entropy deviations to state distance, and show that these results are stable under unital completely positive maps. The analysis is self-contained and relies on convex duality, relative entropy, and Pinsker-type inequalities, providing a rigorous and unified foundation for finite-dimensional maximum-entropy inference. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21095 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of Maximum-Entropy Inference in Finite Dimensions Tian, James Quantum Physics Functional Analysis Primary: 94A17, secondary: 47N50, 81P45 We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints. Given expectation values of finitely many observables, the feasible set of states is convex but typically non-unique. The maximum-entropy principle selects the Gibbs state that agrees with the data while remaining maximally unbiased. We prove that convergence of moments and entropy implies convergence of states in trace norm, derive explicit quantitative bounds linking data and entropy deviations to state distance, and show that these results are stable under unital completely positive maps. The analysis is self-contained and relies on convex duality, relative entropy, and Pinsker-type inequalities, providing a rigorous and unified foundation for finite-dimensional maximum-entropy inference. |
| title | Stability of Maximum-Entropy Inference in Finite Dimensions |
| topic | Quantum Physics Functional Analysis Primary: 94A17, secondary: 47N50, 81P45 |
| url | https://arxiv.org/abs/2510.21095 |