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arXiv · 2504.03488

Hilbert-Schmidt norm estimates for fermionic reduced density matrices

François Louis Antoine Visconti
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Abstract

We prove that the Hilbert-Schmidt norm of $k$-particle reduced density matrices of $N$-body fermionic states is bounded by $C_kN^{k/2}$ - matching the scaling behaviour of Slater determinant states. This generalises a recent result of Christiansen (2024) on 2-particle reduced density matrices to higher-order density matrices. Moreover, our estimate directly yields a lower bound on the von Neumann entropy and the 2-R\'enyi entropy of reduced density matrices, thereby providing further insight into conjectures of Carlen-Lieb-Reuvers (2016,2018).

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François Louis Antoine Visconti. 2025-04-04. Hilbert-Schmidt norm estimates for fermionic reduced density matrices. https://arxiv.org/abs/2504.03488

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