Spectral moments of Bures-Hall ensemble and applications to entanglement entropy
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911413646131200 |
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| author | Wei, Linfeng Huang, Youyi Wei, Lu |
| author_facet | Wei, Linfeng Huang, Youyi Wei, Lu |
| contents | We study spectral moments of the Bures-Hall random matrices ensemble. The main result establishes a recurrence relation for the $k$-th spectral moment valid for a real-valued $k$, in contrast to prevailing results in the literature of different ensembles of assuming an integer $k$. The key to establish the recurrence relation is the obtained Christoffel-Darboux formulas of correlation kernels of the ensemble that avoid tedious summations. As an application of our spectral moment results, we re-derive the formulas of average von Neumann entropy and quantum purity of Bures-Hall ensemble conjectured by Ayana Sarkar and Santosh Kumar. This work is dedicated to the memory of Santosh Kumar. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00955 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral moments of Bures-Hall ensemble and applications to entanglement entropy Wei, Linfeng Huang, Youyi Wei, Lu Mathematical Physics Information Theory Quantum Physics We study spectral moments of the Bures-Hall random matrices ensemble. The main result establishes a recurrence relation for the $k$-th spectral moment valid for a real-valued $k$, in contrast to prevailing results in the literature of different ensembles of assuming an integer $k$. The key to establish the recurrence relation is the obtained Christoffel-Darboux formulas of correlation kernels of the ensemble that avoid tedious summations. As an application of our spectral moment results, we re-derive the formulas of average von Neumann entropy and quantum purity of Bures-Hall ensemble conjectured by Ayana Sarkar and Santosh Kumar. This work is dedicated to the memory of Santosh Kumar. |
| title | Spectral moments of Bures-Hall ensemble and applications to entanglement entropy |
| topic | Mathematical Physics Information Theory Quantum Physics |
| url | https://arxiv.org/abs/2602.00955 |