Abstract We prove that the Hilbert–Schmidt norm of k -particle reduced density matrices of N -body fermionic states is bounded from above by CₖN^k/2 C k N k / 2 - 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-Rényi entropy of reduced density matrices, thereby providing further insight into conjectures of Carlen–Lieb–Reuvers 2, 8.
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François L. A. Visconti
Annales Henri Poincaré
Ludwig-Maximilians-Universität München
LMU Klinikum
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François L. A. Visconti (Mon,) studied this question.
www.synapsesocial.com/papers/69c37be2b34aaaeb1a67eb5c — DOI: https://doi.org/10.1007/s00023-026-01686-z
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