Vacuum as a less hostile environment to entanglement

We derive sufficient conditions for infinite-dimensional systems whose entanglement is not completely lost in a finite time during its decoherence by a passive interaction with local vacuum environments. The sufficient conditions allow us to clarify a class of bipartite entangled states which preserve their entanglement or, in other words, are tolerant against decoherence in a vacuum. We also discuss such a class for entangled qubits.

Figure 1

The logarithmic negativity (a) and the minimal eigenvalue (b) of the state obtained by inverse decoherence with parameter $\eta$.

Figure 2

(Color online) The real and imaginary parts of the particular separable density matrix under consideration are depicted as (a) and (b), respectively. The density matrix of the (still physical) state affected by the inverse decoherence map with $\eta =0.64$ is shown in (c) (real part) and (d) (imaginary part). The logarithmic negativity of this state is $E_{\mathcal{N}}\approx 0.06$.