Simple proof of the robustness of Gaussian entanglement in bosonic noisy channels

TL;DR

This paper proves that Gaussian states are the most robust bipartite continuous-variable states against entanglement loss in Markovian Gaussian channels, confirming a recent conjecture through a rigorous proof.

Contribution

It provides a simple proof confirming Gaussian states' extremality and robustness against disentanglement in noisy bosonic channels, validating previous conjectures.

Findings

Gaussian states are most robust against disentanglement in Markovian Gaussian channels.

The proof confirms the extremality of Gaussian states in this context.

The result validates a recent conjecture about Gaussian state robustness.

Abstract

The extremality of Gaussian states is exploited to show that Gaussian states are the most robust, among all possible bipartite continuous-variable states at fixed energy, against disentanglement due to noisy evolutions in Markovian Gaussian channels involving dissipation and thermal hopping. This proves a conjecture raised recently in [M. Allegra, P. Giorda, and M. G. A. Paris, Phys. Rev. Lett. {\bf 105}, 100503 (2010)], providing a rigorous validation of the conclusions of that work. The problem of identifying continuous variable states with maximum resilience to entanglement damping in more general bosonic open system dynamical evolutions, possibly including correlated noise and non-Markovian effects, remains open.