Hilbert–Schmidt Norm Estimates for Fermionic Reduced Density Matrices

Key Points

• The study aims to establish bounds for the Hilbert–Schmidt norm of k-particle reduced density matrices of N-body fermionic states.
• Proving upper bounds on the Hilbert–Schmidt norm for k-particle reduced density matrices.
• Generalizing existing results on 2-particle reduced density matrices to higher order density matrices.
• Analyzing the implications for von Neumann and 2-Rényi entropy.
• Established an upper bound of C_kN^(k/2) for the Hilbert–Schmidt norm.
• Confirmed that this scaling matches that of Slater determinant states.
• Provided lower bounds on von Neumann and 2-Rényi entropy for the reduced density matrices.