Duality of reduced density matrices and their eigenvalues

Abstract

For states of quantum systems of $N$ particles with harmonic interactions we prove that each reduced density matrix $\rho$ obeys a duality condition. This condition implies duality relations for the eigenvalues ${\lambda }_k$ of $\rho$ and relates a harmonic model with length scales $l_1,l_2,\dots ,l_N$ with another one with inverse lengths $1/l_1,1/l_2,\dots ,1/l_N$. Entanglement entropies and correlation functions inherit duality from $\rho$. Self-duality can only occur for noninteracting particles in an isotropic harmonic trap.

References in corpus (5)

• The Pauli principle revisited
• The Spectra of Density Operators and the Kronecker Coefficients of the Symmetric Group
• Pinning of Fermionic Occupation Numbers
• Quantum state transformations and the Schubert calculus
• Connecting N-representability to Weyl's problem: The one particle density matrix for N = 3 and R = 6

Cited by in corpus (1)

• Pinning of fermionic occupation numbers: Higher spatial dimensions and spin