Title: Hilbert-Schmidt norm estimates for fermionic reduced density matrices Show Chinese title

Title: Hilbert-Schmidt 范数估计对于费米子约化密度矩阵

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). Show Chinese abstract

Abstract: 我们证明了 $k$-粒子约化密度矩阵的 Hilbert-Schmidt 范数对于 $N$-体费米态是有限的，其上限为 $C_kN^{k/2}$ - 与 Slater 行列式态的尺度行为相匹配。 这一结果推广了 Christiansen (2024) 关于 2-粒子约化密度矩阵的近期结果到更高阶的密度矩阵。 此外，我们的估计直接给出了约化密度矩阵的 von Neumann 熵和 2-Rényi 熵的下界，从而进一步揭示了 Carlen-Lieb-Reuvers (2016,2018) 的猜想。