Abrupt changes in the dynamics of quantum disentanglement

The evolution of the lower bound of entanglement proposed by Chen et al. [Phys. Rev. Lett. 95, 210501 (2005)] in high-dimensional bipartite systems under dissipation is studied. Discontinuities for the time derivative of this bound are found depending on the initial conditions for entangled states. These abrupt changes along the evolution of the entanglement bound appear as precursors of sudden death.

Figure 1

Evolution of $\Lambda \left(t\right)$ for the initial mixed state of Eq. (4) with $\lambda =0.1$ as a function of the adimensional time $\Gamma t$.

Figure 2

Relevant eigenvalues of the matrix $M$ for the case shown in Fig. 1.

Figure 3

Times for sudden changes in the dynamics of the LBOE as a function of the parameter $\lambda$. The solid line corresponds to the first sudden change, dashed line corresponds to the second sudden change, and dot-dashed line corresponds to the sudden death.

Figure 4

Relevant eigenvalues of partial transpose matrix ${\rho }^{T_A}$.

Figure 5

Evolution of $\Lambda \left(t\right)$ for the case shown in Fig. 1 (dashed line) for $\lambda =0.15$ and for a initial state in the subspace $\{\mid 11⟩,\mid 22⟩\}$ (solid line) for $\chi =0.2$.

Figure 6

Evolution of $\Lambda \left(t\right)$ for the nonmaximal pure state. The dashed line corresponds to $\alpha =0.2386$, $\beta =0.9545$, and $\gamma =0.1790$, and the solid line corresponds to $\alpha =0.1790$, $\beta =0.2386$, and $\gamma =0.9545$.