Duality of reduced density matrices and their eigenvalues - Schilling, C; Schilling, R (IOP Publishing, 2014)
For states of quantum systems of N particles with harmonic interactions we prove that each reduced density matrix ρ obeys a duality condition. This condition implies duality relations for the eigenvalues λk of ρ and relates a harmonic model with length scales ${{\ell }_{1}},{{\ell }_{2}},… ,{{\ell }_{N}}$ with another one with inverse lengths $1/{{\ell }_{1}},1/{{\ell }_{2}},… ,1/{{\ell }_{N}}$. Entanglement entropies and correlation functions inherit duality from ρ. Self-duality can only occur for noninteracting particles in an isotropic harmonic trap.