Quantum to classical transition and entanglement sudden death in Gaussian states under local heat bath dynamics

TL;DR

This paper investigates how entanglement in two-mode Gaussian states disappears suddenly under local thermal baths, linking the phenomenon to the quantum-to-classical transition and extending results to multi-mode systems.

Contribution

It provides a method to calculate the entanglement sudden death time in Gaussian states using Simon’s criterion, generalizing to multi-mode systems and connecting to qubit system results.

Findings

Entanglement sudden death occurs at a calculable time based on covariance matrices.

Results are consistent for zero and finite temperature baths.

The approach extends to multi-mode Gaussian states, mirroring qubit system behaviors.

Abstract

Entanglement sudden death in spatially separated two-mode Gaussian states coupled to local thermal and squeezed thermal baths is studied by mapping the problem to that of the quantum-to-classical transition. Using Simon's criterion concerning the characterisation of classicality in Gaussian states, the time to ESD is calculated by analysing the covariance matrices of the system. The results for the two-mode system at T=0 and T>0 for the two types of bath states are generalised to $n$-modes, and are shown to be similar in nature to the results for the general discrete $n$-qubit system.