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Hilbert-Schmidt Norm Estimates for Fermionic Reduced Density Matrices
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DOI：10.1007/s00023-026-01686-z.png)
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Abstract
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We prove that the Hilbert-Schmidt norm of k-particle reduced density matrices of N-body fermionic states is bounded from above by CkNk/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_kN<^>{k/2}$$\end{document} - matching the scaling behaviour of Slater determinant states. This generalises a recent result of Christiansen [3] 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 & eacute;nyi entropy of reduced density matrices, thereby providing further insight into conjectures of Carlen-Lieb-Reuvers [2, 8].
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