Typical entanglement for Gaussian states
Abstract
We consider ensembles of bipartite states resulting from a random passive Gaussian unitary applied to a fiducial pure Gaussian state. We show that the symplectic spectra of the reduced density operators concentrate around that of a thermal state with the same energy. This implies, in particular, concentration of the entanglement entropy as well as other entropy measures. Our work extends earlier results on the typicality of entanglement beyond the two ensembles and the reduced purity measure considered in [A. Serafini, O. C. O. Dahlsten, D. Gross, and M. B. Plenio, J. Phys. A: Math. Theor., 40(31):9551 (2007)].
Cite
@article{arxiv.1903.04126,
title = {Typical entanglement for Gaussian states},
author = {Motohisa Fukuda and Robert Koenig},
journal= {arXiv preprint arXiv:1903.04126},
year = {2019}
}
Comments
19pages. Other materials: one Mathematica notebook, two Python files and one PDF file for the manual. V2: ancillary files uploaded, reference corrected