Sudden change in dynamics of genuine multipartite entanglement of cavity-reservoir qubits

We study the dynamics of genuine multipartite entanglement for a system of four qubits. Using a computable entanglement monotone for multipartite systems, we investigate the as yet unexplored aspects of a cavity-reservoir system of qubits. For one specific initial state, we observe a sudden transition in the dynamics of genuine entanglement for the four qubits. This sudden change occurs only during a time window where neither cavity-cavity qubits nor reservoir-reservoir qubits are entangled. We show that the sudden change in dynamics of this specific state is extremely sensitive to white noise.

Figure 1

$E$ monotone is plotted against parameter $\kappa t$ for cavity-cavity qubits (black solid line), reservoir-reservoir qubits (red dashed line), and all four qubits (blue dashed-dotted line) for $\alpha =\sqrt{2/3}$ and $\beta =\sqrt{1/3}$. See text for more description.

Figure 2

$E$ monotone is plotted against parameter $\kappa t$ for cavity-cavity qubits (black solid line), reservoir-reservoir qubits (red dashed line), and all four qubits (blue dashed-dotted line) for $\alpha =\sqrt{1/3}$ and $\beta =\sqrt{2/3}$.

Figure 3

$E$ monotone is plotted against parameter $\kappa t$ for cavity-cavity qubits (black solid line), reservoir-reservoir qubits (red dashed line), and all four qubits (blue dashed-dotted line). We take $\alpha =\sqrt{1/10}$ and $\beta =3\sqrt{1/10}$. In the time window when there is no entanglement between cavity qubits and reservoir qubits, the multipartite entanglement exhibits an abrupt change to a value that remains constant in that window.

Figure 4

Same caption as Fig. 3, except we take $\alpha =\sqrt{1/26}$ and $\beta =5\sqrt{1/26}$. See the text for more descriptions.

Figure 5

Entanglement monotone for cavity qubits (solid line), reservoir qubits (dashed line), and the collective state of four qubits (dashed-dotted line) is plotted against parameter $\kappa t$ for Werner states with $p=0.45$.

Figure 6

Same caption as Fig. 5 but for $p=0.75$.

Figure 7

The entanglement monotone is plotted for cavity-cavity (solid line), reservoir-reservoir (dashed line), and four qubits (dashed-dotted line) for states (21) for $a=1$.

Figure 8

Same caption as Fig. 7 but for $a=0.5$.

Figure 9

Entanglement monotone is plotted for cavity-cavity (solid line), reservoir-reservoir (dashed line), and four qubits (dashed-dotted line) for states (24) for $c=0.6$.

Figure 10

Same caption as Fig. 9 but for $c=0.45$.

Figure 11

Entanglement monotone is plotted for cavity-cavity (solid line), reservoir-reservoir (dashed line), and four qubits (dashed-dotted line) for states [Eq. (27)] for $f=0.999$.

Figure 12

The quantities $x={\xi }^2\left(t\right),y={\chi }^2\left(t\right)$, and $z=\xi \left(t\right)\chi \left(t\right)$ are plotted against parameter $\kappa t$ for interval $\kappa t\in [0.46,0.99]$.