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arXiv · 2602.00955

Spectral moments of Bures-Hall ensemble and applications to entanglement entropy

Linfeng Wei·Youyi Huang·Lu Wei
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Abstract

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.

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Linfeng Wei, Youyi Huang, Lu Wei. 2026-02-01. Spectral moments of Bures-Hall ensemble and applications to entanglement entropy. https://arxiv.org/abs/2602.00955

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