Do all states undergo sudden death of entanglement at finite temperature?

TL;DR

This paper investigates how quantum entanglement between two-level systems decays at finite temperature, showing that entanglement always experiences sudden death in finite time for a broad class of initial states.

Contribution

It proves that entanglement sudden death occurs at finite temperature for all states that had long-lived entanglement at zero temperature, extending previous zero-temperature results.

Findings

Entanglement always undergoes sudden death at finite temperature.

All initially entangled states considered become disentangled in finite time.

The result is demonstrated through a specific example.

Abstract

In this paper we consider the decay of quantum entanglement, quantified by the concurrence, of a pair of two-level systems each of which is interacting with a reservoir at finite temperature T. For a broad class of initially entangled states, we demonstrate that the system always becomes disentangled in a finite time i.e."entanglement sudden death" (ESD) occurs. This class includes all states which previously had been found to have long-lived entanglement in zero temperature reservoirs. Our general result is illustrated by an example.