Sudden death of entanglement at finite temperature

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 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.