The separability of tripartite Gaussian state with amplification and amplitude damping

TL;DR

This paper investigates how tripartite Gaussian states evolve under amplification, damping, and noise, deriving conditions for their complete separability or entanglement over time.

Contribution

It provides explicit conditions for the full separability and entanglement of tripartite Gaussian states under realistic environmental interactions.

Findings

Derived time-dependent correlation matrix for the state

Established criteria for full separability

Established criteria for full entanglement

Abstract

Tripartite three mode Gaussian state undergoes parametric amplification and amplitude damping as well as thermal noise is studied. In the case of a state totally symmetrically interacting with the environment, the time dependent correlation matrix of the state in evolution is given. The conditions for fully separability and fully entanglement of the final tripartite three mode Gaussian state are worked out.