Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems

We study the entanglement dynamics of two cavities interacting with independent reservoirs. Expectedly, as the cavity entanglement is depleted, it is transferred to the reservoir degrees of freedom. We find also that when the cavity entanglement suddenly disappears, the reservoir entanglement suddenly and necessarily appears. Surprisingly, we show that this entanglement sudden birth can manifest before, simultaneously, or even after entanglement sudden death. Finally, we present an explanatory study of other entanglement partitions and of higher dimensional systems.

Figure 1

Evolution of two-qubit concurrence ${\mathcal{C}}_{c_1{c}_2}$ (solid line) and ${\mathcal{C}}_{r_1{r}_2}$ (dashed line), for the initial state of Eq. (4) with $\alpha =1/\sqrt{3}$ and $\beta =\sqrt{2/3}$.

Figure 2

Evolution of two-qubit concurrence for different partitions: ${\mathcal{C}}_{c_1{c}_2}$ (solid line), ${\mathcal{C}}_{r_1{r}_2}$ (dashed line), ${\mathcal{C}}_{c_1{r}_1}$ (dot-dashed line), and ${\mathcal{C}}_{c_1{r}_2}$ (dotted line), for the initial state of Eq. (4) with $\alpha =1/\sqrt{10}$ and $\beta =3/\sqrt{10}$.

Figure 3

Evolution of entanglement for different partitions: (a) $c_1\otimes r_1\otimes c_2\otimes r_2$, (b) $(c_1\otimes r_1)\otimes (c_2\otimes r_2)$, (c) $(c_1\otimes c_2)\otimes (r_1\otimes r_2)$, (d) $(c_1\otimes r_2)\otimes (c_2\otimes r_1)$, (e) $c_1\otimes (r_1\otimes c_2\otimes r_2)$, and (f) $r_1\otimes (c_1\otimes c_2\otimes r_2)$, for the initial state of Eq. (4) with $\alpha =1/\sqrt{10}$ and $\beta =3/\sqrt{10}$.

Figure 4

Evolution of two-qutrit LBOE for different partitions: ${\Lambda }_{c_1{c}_2}$ (solid line), ${\Lambda }_{r_1{r}_2}$ (dashed line), ${\Lambda }_{c_1{r}_1}$ (dot-dashed line), and ${\Lambda }_{c_1{r}_2}$ (dotted line), for the initial state of Eq. (12) with $\alpha =1/\sqrt{38}$, $\beta =1/\sqrt{38}$, and $\gamma =6/\sqrt{38}$.

Figure 5

Evolution of the LBOE ${\Lambda }_{c_1{c}_2}$ and ${\Lambda }_{r_1{r}_2}$ (solid lines) and ${\Lambda }_{c_1{r}_1}$ (dashed lines), for initial state $|{\Psi }_0⟩$ with $d=2$, 3, and 4. Probability amplitudes ${\alpha }_k$ with $k=0,1,\dots ,d-1$ are all equal to $1/\sqrt{\sum _{k=0}^d|{\alpha }_k{|}^2}$ and ${\alpha }_d=2^{d-1}{\alpha }_0$.