Ultimate entanglement robustness of two-qubit states against general local noises

We study the problem of optimal preparation of a bipartite entangled state, which remains entangled the longest time under action of local qubit noises. We show that for unital noises, such a state is always maximally entangled, whereas for nonunital noises, it is not. We develop a decomposition technique relating nonunital and unital qubit channels, based on which we find the explicit form of the ultimately robust state for general local noises. We illustrate our findings by amplitude damping processes at finite temperature, for which the ultimately robust state remains entangled up to two times longer than conventional maximally entangled states.

Figure 1

Transmission of entangled state through local quantum channels.

Figure 2

Graphical solution of Eq. (26). All quantities are dimensionless.

Figure 3

Evolution of negativity under local generalized amplitude damping noise $\mathrm{\Phi }\left(t\right)\otimes \mathrm{\Phi }\left(t\right)$ with $w=0.01$ for the following initial states: the maximally entangled state (red dashed curve) and the ultimately robust state (blue solid curve). $\gamma t$ is dimensionless time. The dotted line represents a collection of negativities for states $\mathrm{\Phi }\left(t\right)\otimes \mathrm{\Phi }\left(t\right)\left[\right|{\psi }_t\rangle \langle {\psi }_t\left|\right]$, where the interpolating initial state $|{\psi }_t\rangle$ is given by Eq. (50).