Mixedness and entanglement for two-mode Gaussian states

TL;DR

This paper analytically studies the dynamics of entanglement and mixedness in two-mode Gaussian states, revealing conditions for entanglement sudden death and the influence of initial impurities.

Contribution

It provides analytical expressions for entanglement dynamics and ESD conditions in two-mode Gaussian states, linking initial impurities to entanglement suppression.

Findings

Entanglement sudden death always occurs at zero temperature for certain symmetric states.

Analytical formulas for the time of ESD are derived.

Initial impurities in single modes suppress initial entanglement.

Abstract

We analytically exploit the two-mode Gaussian states nonunitary dynamics. We show that in the zero temperature limit, entanglement sudden death (ESD) will always occur for symmetric states (where initial single mode compression is $z_0$) provided the two mode squeezing $r_0$ satisfies $0 < r_0 < 1/2 \log (\cosh (2 z_0)).$ We also give the analytical expressions for the time of ESD. Finally, we show the relation between the single modes initial impurities and the initial entanglement, where we exhibit that the later is suppressed by the former.