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arXiv · 1408.3128

Duality of reduced density matrices and their eigenvalues

Christian Schilling·Rolf Schilling
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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, \ldots, l_N $ with another one with inverse lengths $1/l_1, 1/l_2,\ldots, 1/l_N$. Entanglement entropies and correlation functions inherit duality from $\rho$. Self-duality can only occur for noninteracting particles in an isotropic harmonic trap.

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Christian Schilling, Rolf Schilling. 2014-08-13. Duality of reduced density matrices and their eigenvalues. https://doi.org/10.1088/1751-8113/47/41/415305

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