Robust multipartite entanglement generation via a collision model

We examine a simple scheme to generate genuine multipartite entangled states across disjoint qubit registers. We employ a shuttle qubit that is sequentially coupled, in an energy preserving manner, to the constituents within each register through rounds of interactions. We establish that stable $W$-type entanglement can be generated among all qubits within the registers. Furthermore, we find that the entanglement is sensitive to how the shuttle is treated, showing that a significantly larger degree is achieved by performing projective measurements on it. Finally, we assess the resilience of this entanglement generation protocol to several types of noise and imperfections, showing that it is remarkably robust.

Figure 1

Schematic of the setting. We consider two distinct registers of qubits, $r_1,r_2$ and $s_1,s_2$, whose mutual interaction is mediated by an ancillary qubit $A$. As $A$ plays the role of a shuttle connecting disjoint parts of the system, we restrict its interactions to be weak, taking $\gamma =0.05$ in Eq. (1), while the interactions within a given register can be of arbitrary strength but are restricted to be between nearest neighbors. We discretize the time such that steps (i) to (iv) represent the series of interactions realizing a single iteration of the process. The system exhibits quasiperiodicity after $\sim 45$ iterations.

Figure 2

(a) Bipartite entanglement, (b) tripartite entanglement, and (c) quadripartite entanglement. In all panels register qubits are initialized in $\left|0\right.〉$, while the shuttle's initial state is $\left|1\right.〉$. The shuttle-register interaction is weak, $\gamma =0.05$ while we assume strong interactions within both registers, $\gamma =0.95\frac{\pi }{2}$. The upper curves in each panel correspond to a projective measurement performed on the shuttle, while the lower curves correspond to tracing over the shuttle's degrees of freedom.

Figure 3

As for Fig. 2, except taking the interaction strength within the registers to be zero.

Figure 4

Dynamics of the absolute values of coefficients $b_i$ in Eq. (11) for (a) strong and (b) zero intraregister interactions. Note that for $b_i\sim 0.5$ indicates that we obtained a symmetric $W$ state.

Figure 5

Dynamical entanglement as a function of the probability, $p$, that the shuttle-register interaction is missed. (a) Bipartite entanglement between $r_1$ and $s_1$ when the shuttle is traced out and (b) after a projective measurement is performed on the shuttle. (c) Tripartite negativity between qubits $r_1, r_2$, and $s_1$ when the shuttle is traced out and (d) after a projective measurement is performed on the shuttle. (e) Quadripartite entanglement after the shuttle is traced out for $p=0, p=0.3$, and $p=0.8$ and (f) after a projective measurement on the shuttle for $p=0, p=0.3$, and $p=0.8$. In all panels we consider strong interactions within the registers, assume the register qubits' initial states to be $\left|0\right.〉$, and the shuttle's initial state is $\left|1\right.〉$.

Figure 6

Thermal effects on generated entanglement after $n=25$ iterations. Qubits within both registers are initially in Gibbs states at temperatures $T_1$ and $T_2$ for $r$ and $s$, respectively, while the shuttle is initially in its excited state $\left|1\right.〉$. We consider strong interactions within the registers, $\gamma =0.95\frac{\pi }{2}$ and weak shuttle-register interactions $\gamma =0.05$. In both panels solid curves correspond to a projective measurement on the shuttle, while dashed curves correspond to tracing over the shuttle's degrees of freedom. Temperature of $r$-register (a) $T_1=0$ and (b) $T_1=1$.

Figure 7

Effects of qubit dephasing on (a) bipartite entanglement between $r_1$ and $s_1$. (b) Tripartite entanglement between $r_1, r_2$ and $s_1$. (c) Quadripartite entanglement across both registers. In all panels we assume strong interactions between register qubits $\gamma =0.95\frac{\pi }{2}$, weak shuttle-register interactions $\gamma =0.05$, all register qubits are initialized in state $\left|0\right.〉$, shuttle qubit is initialized in state $\left|1\right.〉$, and a projective measurement is performed on the shuttle.