# Typical entanglement for Gaussian states

## TL;DR

This paper demonstrates that for Gaussian states subjected to random passive Gaussian unitaries, the entanglement properties concentrate around those of a thermal state with the same energy, extending typicality results in quantum entanglement.

## Contribution

It extends the understanding of entanglement typicality to Gaussian states under passive unitaries, showing spectral concentration around thermal states.

## Key findings

- Symplectic spectra concentrate around thermal states.
- Entanglement entropy shows concentration behavior.
- Results extend previous entanglement typicality studies.

## 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)].