Classical and quantum correlations under decoherence

Recently some authors have pointed out that there exist nonclassical correlations which are more general, and possibly more fundamental, than entanglement. For these general quantum correlations and their classical counterparts, under the action of decoherence, we identify three general types of dynamics that include a peculiar sudden change in their decay rates. We show that, under suitable conditions, the classical correlation is unaffected by decoherence. Such dynamic behavior suggests an operational measure of both classical and quantum correlations that can be computed without any extremization procedure.

Figure 1

Classical $C\left[\epsilon \left({\rho }_{AB}\right)\right]$ (dashed line), quantum $Q\left[\epsilon \left({\rho }_{AB}\right)\right]$ (solid line), and total $I\left[\epsilon \left({\rho }_{A:B}\right)\right]$ (dotted line) correlations under phase flip. We have set, in this figure, $c_1=0.06$, $c_2=0.42$, and $c_3=0.30$. For this state the sudden change occurs at $p_{SC}=0.15$ and $\mathcal{Q}$ is greater than $\mathcal{C}$ for $0.09\le p\le 0.20$. At $p=0.09$ and $p=0.20$, we have $\mathcal{Q}\left[\epsilon \left({\rho }_{AB}\right)\right]=\mathcal{C}\left[\epsilon \left({\rho }_{AB}\right)\right]=\mathcal{I}\left[\epsilon \left({\rho }_{A:B}\right)\right]/2$, as happens for pure states.

Figure 2

Sudden change parametrized time. $p_{SC}$ as a function of $c_1$ and $c_2$, for $c_3=0.1$, under a phase flip channel. In the regions where $p_{SC}=0$ or $p_{SC}=1$ there is no sudden change.