Multipartite Entanglement Detection in Bosons

We propose a simple quantum network to detect multipartite entangled states of bosons and show how to implement this network for neutral atoms stored in an optical lattice. We investigate the special properties of cluster states, multipartite entangled states, and superpositions of distinct macroscopic quantum states that can be identified by the network.

Figure 1

Network of BS acting on pairs of identical bosons. The two rows of $N$ atoms, labeled I and II, respectively, are identical, and the state of each of the rows is ${\rho }_{123\cdots N}$. The total state of the system is ${\rho }_{123\cdots N}\otimes {\rho }_{123\cdots N}$.

Figure 2

In (a), we plot the violation $V$ of the inequalities Eq. (2), $V_1=\mathrm{T}\mathrm{r}({\rho }_{123}^2)-\mathrm{T}\mathrm{r}({\rho }_{12}^2)$ (dashed line), $V_2=\mathrm{T}\mathrm{r}({\rho }_{12}^2)-\mathrm{T}\mathrm{r}({\rho }_1^2)$ (gray line), and $V_3=\mathrm{T}\mathrm{r}({\rho }_{12}^2)-\mathrm{T}\mathrm{r}({\rho }_2^2)$ (solid line), as a function of the phase $\varphi$, for $N=3$ atoms. Whenever $V>0$, entanglement is detected by our network. In (b), we plot the purity ${\Pi }_{N-m}$ for $m=1$ (solid black line), $m=7$ (dashed black line ), $m=14$ (solid gray line), and $m=20$ (dashed gray line), as a function of $ϵ$, for $N=300$ atoms.