A Berry-Esseen Bound for Quantum Lattice Systems
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918484932296704 |
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| author | Cramer, Marcus Brandão, Fernando G. S. L. Guţă, Mădălin Alhambra, Álvaro M. Scandi, Matteo |
| author_facet | Cramer, Marcus Brandão, Fernando G. S. L. Guţă, Mădălin Alhambra, Álvaro M. Scandi, Matteo |
| contents | It is expected that the statistical fluctuations of local observables in large quantum systems obey the central limit theorem, and approximate a normal distribution as their size grows. Here, we prove a version of the Berry-Esseen theorem for quantum lattice systems, which strengthens that central limit theorem by providing a rigorous convergence estimate towards the normal distribution for large but finite system size. Given a local quantum Hamiltonian on $N$ particles and a quantum state with a finite correlation length, the result states that the measurement of local observables such as the energy follows a normal distribution, up to an error scaling as $\mathcal{O}\left(N^{-\frac{1}{2}} \text{polylog}(N)\right)$, which is optimal up to logarithmic factors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03829 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Berry-Esseen Bound for Quantum Lattice Systems Cramer, Marcus Brandão, Fernando G. S. L. Guţă, Mădălin Alhambra, Álvaro M. Scandi, Matteo Quantum Physics Statistical Mechanics It is expected that the statistical fluctuations of local observables in large quantum systems obey the central limit theorem, and approximate a normal distribution as their size grows. Here, we prove a version of the Berry-Esseen theorem for quantum lattice systems, which strengthens that central limit theorem by providing a rigorous convergence estimate towards the normal distribution for large but finite system size. Given a local quantum Hamiltonian on $N$ particles and a quantum state with a finite correlation length, the result states that the measurement of local observables such as the energy follows a normal distribution, up to an error scaling as $\mathcal{O}\left(N^{-\frac{1}{2}} \text{polylog}(N)\right)$, which is optimal up to logarithmic factors. |
| title | A Berry-Esseen Bound for Quantum Lattice Systems |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2605.03829 |